Advancing Physics Chapter 2

1 Advancing Physics

Revision questionsQuestion 20S: Short Answer

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These questions are on electric current, potential difference and power.

Estimating your electricity billSandra wants to budget for paying the electricity bill on her small new flat. For cooking she mainlyuses a microwave oven rated at 1 kW to reheat chilled meals, 'bake' potatoes etc. On average shewill use this cooker for 10 minutes a day. She also assumes she will use a kettle (rated at 3.3 kW)and a toaster (rated at 500 W) daily for the about the same period of time.

1. Calculate how many kilowatt-hours Sandra uses daily for preparing meals and snacks.

2. She remembers to include the cost of lighting: she has 100 W bulbs throughout the flat andexpects to have one of the lights on in the evening for 3 hours.

Work out the number of kilowatt-hours Sandra uses daily on lighting.

3. Estimate Sandra's quarterly bill assuming one quarter = 90 days and the cost of electricity is 10 p/ kilowatt-hour.

4. If you wish, add on your own estimates for weekly ironing and vacuuming.

Cost of an electrically heated shower5. In your student 'digs', you have to put a 20 p coin in a slot if you want to have a five minute

shower. You note that 'Power Rating = 9 kW' is marked on the shower fitting. The last electricitybill to your home stated that one unit of electricity cost 10 p. Is the shower good value? Justifyyour answer with a calculation.

Torch Bulb

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3 V; 0.5 A is written on the packet of torch bulbs.

6. Use your ideas about electrons to describe the mechanism of the energy transfer when the torchis 'on'.

7. Calculate the power conversion for the bulb in normal use.

8. The life of the bulb is approximately 10 hours.

How much energy will it have dissipated in its lifetime?

Kinds of light bulbQuestion 30S: Short Answer


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People use electric light bulbs for many purposes, from a torch used to light up a path home, toaircraft searchlights. These lamps differ tremendously in the power they use.

1. All bulbs are stamped with two different values, for instance 36 W, 12 V. What do these numberstell you?

2. You can also use these values to calculate the current and the resistance of the bulb filament.The table below shows these values for five different bulbs. Use a suitable formula to calculatethe missing values.

Bulb Power /W

p.d. / V Current /A

Resistance /

Headlamp 36 12 4

Torch bulb 0.09 3 0.03

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Bulb Power /W

p.d. / V Current /A

Resistance /

Filament bulb 100 230 529

Flashlight bulb 4.5 9 0.5

Energy Saving bulb 24 230

Fuse protection3. Explain why appliances are protected by a fuse and explain how the fuse provides this protection.

4. The table shows the electrical power rating and voltage as marked on a number of appliances.Calculate the operating current of each appliance. Suggest a suitable fuse value for eachappliance choosing from the fuse values given.

Appliances Powerrating

p.d. / V Operatingcurrent /A

Suggested fuse values choosingfrom 3 A; 5 A; 13 A

Iron 1200 W 230

Vacuum cleaner 900 W 230

Headlamp 48 W 12

Jug kettle 2.4 kW 230

Radio 100 W 230

Travel kettle 340 W 120

Microwavecooker

1.4 kW 230

Measuring potential differenceA pupil wants to measure the potential difference across a battery connected to a circuit:

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A B C

F E D

2 k10 V

4 k

5. What instrument should he/she use?

6. The pupil notices that when the meter is put across the terminals AF, BE, CD in turn, the readingis always the same. Why is that so?

7. State and account for the voltmeter readings when placed across FE or AC.

A portable radioYou buy a new portable radio. It is powered by eight cells and there is a diagram printed on thebattery chamber to show you how to fit the cells:

1.5 V 8 R14Battery supply

8. What is the total potential difference of this arrangement of cells?

9. This radio can also be connected to the 240 V a.c. mains supply which is far too large for thisradio to be used directly. What component must be included inside the radio to change theincoming supply to 12 V?

10. Battery and mains supplies vary in potential difference. State one other significant difference.

5 Advancing Physics

Ions in chemical cells:Large and small numbers 1Question 40S: Short Answer

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These problems are intended to help you practice calculations with large numbers of conductingparticles and small amounts of charge found in a variety of examples of electrical conduction.

Chemical cellsA typical chemical cell gives charges a rather low energy, hence cells have modest voltage values,but they can produce substantial electron flows by reacting chemicals in large numbers of atoms persecond.

magnitude of e = 1.6 10–19 C

NA = 6.0 1023 particles / mole

Molar mass of zinc = 65.4 grams

In a chemical cell, the energy released by chemical attack on a metal, say zinc, as in many chemicalreactions, is about 300 kJ per mole of metal attacked.

1. Calculate the charge carried by a mole of electrons (known as a Faraday of charge).

2. What is the potential energy given to each coulomb of charge (i.e. the potential difference)?

Remember that each zinc atom loses 2 electrons to become a Zn2+ ion.

3. The cell delivers a current of 0.2 A; how many electrons does it produce per second?

4. This is a very large number, but how many moles is it?

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5. Chemical cells can produce quite large charge flows for substantial times before their chemicalshave all reacted. If zinc is the metal losing electrons under chemical attack, what mass of zinc isreacting per second to produce this current of 0.2 A? (again remember that each zinc atom loses

2 electrons to become a Zn2+ ion)

6. If the cell contains 5 grams of reactable zinc, for how long could it produce this current beforerunning out?

Ions in x-ray machines:Large and small numbers 2Question 50S: Short Answer

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X-ray machinesAn x-ray machine works by accelerating electrons from a hot cathode through a high voltage in avacuum tube. The fast electrons crash into a metal target, producing a lot of heat and some x-rays,which can be used for medical purposes. The tube current (electrons per second) determines thequantity of x-rays produced and their penetration is determined by the tube potential difference(energy per electron). The current, potential difference and time of exposure are varied by theradiographer to examine different parts of the human body.

Some typical values are:

Examination Voltage / kV Current / mA Time / s

pelvis 65 350 0.8

hand 40 80 0.1

1. How much charge and energy do the electrons in the tube deliver during each exposure?

2. Explain why there are differences in the energy and penetration required.

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3. For the pelvis example, find the number of electrons arriving per second, and the energy of eachelectron.

4. Hence find the number of electrons arriving during the 0.8 s exposure and check that the totalenergy they deliver agrees with your answer to question 1.

Electrons in copper:Large and small numbers 3Question 60S: Short Answer


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Copper conducting

As a rough guide, copper wires can conduct about 10 A mm2 before overheating and there are

approximately 1020 free electrons per mm3 in copper.

Find:

1. The number of electrons per second required to carry a current of 10 A.

2. The length of wire with cross section 1 mm2 containing this number of electrons.

3. The average drift speed of electrons in the wire.

4. If the same wire carried a current of only 10 mA what would the drift speed be, and how longwould it take a typical electron to drift through 1 mm?

8 Advancing Physics

Some circuit problemsQuestion 100S: Short Answer

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1. Print out or copy the table below. Combine the expressions P = I V and V = I R to find the usefulformula for calculating power in terms of current and resistance, and use it to fill in the table.

Resistor value/

Power rating /W

Working current

7.5 0.42 A

47 0.5

3.3 k 2

27 k 9 mA

680 k 0.25

1 30 mA

In an electrical supplies catalogue you will find that resistors are specified according to the maximumpower they can dissipate. You need to use a 5.6 k resistor for a project where the operating currentis 15 mA. It is available with either 1 W or 2 W power rating.

2. Calculate the maximum desirable current for each resistor and decide which one to use.

3. Suggest a reason why the 2 W resistor is physically larger than the 1 W resistor.

Now think about three resistors in parallel.

2 5 10

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4. What is the conductance of each resistor?

5. Which resistor will carry the largest current? (give your reasons but do not use a calculation atthis stage)

6. What is the combined conductance of this arrangement of resistors?

7. The battery is made up of two 1.5 V cells of negligible resistance. Calculate the current throughthe cell.

8. A potentiometer with a length 80 mm is connected to a 12 V supply.

80 mm

V

rheostat sliding contact

+ 12V

– 0Vposition of sliding contact / mm

80

12

Sketch a graph to show how the output voltage varies as the slider is moved along thepotentiometer. Label the axes appropriately.

9. A variable resistor and a fixed resistor of 100 are in series across a 12 V supply.

Sketch the circuit.

Calculate the power that is dissipated by the 100 resistor when the variable resistor is set inturn at 100 , 20 , 50

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Power of appliancesQuestion 110S: Short Answer


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Travelling kettleKasim has to travel abroad as part of his work. Knowing that not all hotels provide a 'Welcome Tray'he buys a travel kettle so he can always make coffee for himself. The kettle is marked:

Open the JPEG file

On the package is written: 'Takes less than 4 minutes to boil on 230 V and 7 minutes on 120 V'

1. Explain the meaning of the power rating: 720 W

2. Why would boiling some water in the kettle in New York (power supply: 120 V) take longer than inBelfast (power supply: 230 V).

3. Calculate the current through the element on each setting.

4. After his trip to New York, Kasim forgets to switch over the voltage setting to 230 V. Why mightthe kettle be damaged by leaving it at the 120 V setting?

5. Suggest a suitable fuse value to use in the plug to protect the kettle from overheating.


Effect of an ammeter in a circuitQuestion 120S: Short Answer


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In a laboratory demonstration a 12 V car battery powers two 12 V, 24 W lamps connected in parallel.

1. Calculate the current through each of the bulbs if they light normally.

2. The current is now measured using an ammeter (of resistance 10 ) which is connected in serieswith each of the bulbs in turn. What will the ammeter read? Comment on your answer.

3. What will the ammeter read when it is placed in series with the battery?

(Neglect any internal resistance of the battery.)

Combining conductancesQuestion 125S: Short Answer


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Conductance or resistance?

When you want to find the total resistance of two or more resistors in parallel it is usually easier towork with conductances.


Try these questions to see why this is so.

1. A component in a circuit has a resistance of 10 . What is its conductance? Make sure you writedown the unit.

2. What is the combined conductance of two 10 resistors in parallel?

10

10

3. What is the conductance of a 100 resistor?

4. Suppose a 100 resistor is connected in parallel with a 10 resistor. What is the totalconductance of the combination?

100

10


5. What is the total resistance of the combination?

6. What do you notice about the total resistance compared to the two separate resistor values?

Circuit resistanceQuestion 130S: Short Answer


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Simplifying circuitsThese are questions about replacing many resistors with one resistor which draws the same currentfrom the cell. Study the circuit diagrams and try to simplify sections of the circuit by putting in anequivalent value resistor. Redraw the diagram for each step until you are reduced to one equivalentresistor before calculating the current. Many of these problems are easier if you think aboutconductance rather than resistance.

For each circuit find the current drawn from the power source.

1.

6 V

5I

4 6


2.

12 V

I

4

12

4

3.

12 V

I5 108

512


4 V

6

3

12

3

In this circuit calculate:

4. The current through the 6 resistor.

5. The potential difference across the 12 resistor.

Combining resistorsQuestion 140S: Short Answer


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Resistor seriesResistors are manufactured in limited values. You will find that the numbers range from 1.0 to 10 in24 steps each differing from the next by about 10%. i.e.:

1.0 1.5 2.2 3.3 4.7 6.8

1.1 1.6 2.4 3.6 5.1 7.5

1.2 1.8 2.7 3.9 5.6 8.2

1.3 2.0 3.0 4.3 6.2 9.1


Two or more of these resistors can be combined to give other values of resistance.

Finding useful combinationsIn the laboratory there are resistors with the values 1 k, 2.2 k, 3.3 k, 4.7 k, 5.6 k and 6.8 k

How can you combine two or more of these resistors when you need a resistance of:

1. 3 k

2. 9 k

3. 500

4. 5 k

5. 4 k

Electrical characteristics of a resistorQuestion 150S: Short Answer


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The table shows the how the current through a resistor of nominal value 4.7 k changes with the p.d.The resistor is designed to have a power dissipation of 1 W.

p.d. / V 5.0 10.0 20.0 30.0 40.0 50.0

current / mA 1.06 2.13 4.25 6.22 7.91 9.41

1. Plot a graph from the data and give a possible explanation for the shape of the graph.


2. Use the graph to find the resistance of the resistor for small applied p.d.s.

3. What is the resistance when the applied p.d. is 50 V?

4. For a particular experiment it is important that the resistance remains within 10% of its statedvalue.

Find the maximum applied p.d. that can be used by selecting a suitable small section of the graphand drawing a resistance versus p.d. graph.

5. What is the theoretical maximum p.d. that can be applied before the resistor is permanentlydamaged?

The algebra of powerQuestion 160S: Short Answer


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These questions lead you through to an understanding of the algebraic relationships between power,current, resistance and potential difference. Look at the example and then answer the questionsthoughtfully.

ExampleThe electrical power P dissipated in a resistance R carrying current I with a p.d. V across it can becalculated in several ways.

Suppose:

6andV12 ,A2W,24 RV P I

1. Using P = I V

W24sJ 24sC 2CJ 12 A2 V12 111 P

2. Since V = I R

RRVP 2)( III I

This should give:


W24 6)A2( 2 P .

3. Since RV /I

RVVRVVP / )/( 2 I

In our example:

W 24 = 6 /V) (12 = 2 P .

How can the power be proportional to resistance R in one relationship and be inversely proportionalto R in another? What do they tell you about different lamps?

P = V 2 / R says that lamps operating at the same potential difference (e.g. all 12 V) will need a lowerresistance to provide greater power. Why? Because at a fixed potential difference you need morecurrent for more power. Lower resistance gives more current.

P = I 2 R says that lamps to operate at the same current will need a larger resistance to provide morepower. Why? The charge flowing per second is the same, so each unit of charge must deliver moreenergy. That means a larger potential difference. For the same current and a larger potentialdifference, the resistance must be larger.

Questions1. Calculate the current through and the resistance of a 500 W stage light lamp with 250 V across it.

2. Calculate the current through and the resistance of a 24 W, 12 V car headlamp. Compare thesevalues with those for the stage light.

Extension: more of the power of algebraFinally if you are getting confident with algebra.

3. Rewrite the equations P = I 2 R and P = V 2 / R replacing resistance R by conductance G.


Tapping off a potential differenceQuestion 170S: Short Answer


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6 V

50 100

A B

A series circuit is connected as shown in the diagram.

1. What is the potential difference between A and B?

2. An additional resistor of 100 is connected in series between the 50 resistor and the cells.What is the potential difference between A and B now?

3. The additional 100 resistor is now connected in parallel with the first 100 resistor. What is thepotential difference between A and B now?

4. A potential divider is made from a 4 k and a 6 k resistor connected in series with a 20 Vsupply. Draw a diagram of the arrangement. What four values of potential difference can betapped off?

5. A student puts a 12 variable resistor in series with a 6 V battery, expecting to get a variable


potential difference.

6 V

12

V

The voltmeter is a high resistance digital multimeter. Explain why the circuit won't work. Draw acircuit which would work.

6. B is the wiper of a 100 rotary potentiometer.

12 V

100

300

A

B

What is the full range of the potential difference that can be tapped off between A and B?

Loading the potential divider


Question 180S: Short Answer


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6 V

250potentiometer

V

10 V

100potentiometer

V

The sliders are at the mid-point of the potential dividers.

1. Find the potential difference recorded by a digital voltmeter of infinite resistance connected as thevoltmeter V in each circuit.

2. The digital voltmeter is replaced by a moving coil voltmeter of resistance 500 . Calculate thenew readings when using this meter.

3. A 100 rotary potentiometer is connected to a 6 V d.c. source with negligible internal resistance.The output required is 3 V. The potentiometer is set using a high impedance digital voltmeter


connected across the output terminals.

A few minutes later someone else checks the output reading using a moving coil voltmeter whichhas a resistance of 100 . What is the reading now?

Controlling a robot armQuestion 200S: Short Answer


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A robot arm contains an 'elbow joint'. The joints can move through 180. The control system of therobot arm needs to know the position of the joint. This robot arm joint contains a 3 k rotarypotentiometer, fixed to the upper arm, whilst the 'forearm' of the robot is attached to the rotating wiperof the potentiometer. A rotary potentiometer consists of a resistor curved into an arc of a circle. Thewiper or sliding contact moves over this resistor. Terminals at the two ends of the resistor connect toa fixed d.c. power supply of 3 V. The rotary potentiometer has a total angle of travel of 300. Assumethat the resistance of the potentiometer is uniform across its length.

robot ‘forearm’

‘elbowjoint’

limit of travel of arm

robot ‘upper arm’

rotarypotentiometer

wiperarm

circularresistor

3 V+ -

output

1. What current flows through the potentiometer?

2. If the robot forearm is vertical, half way through its possible movement, what potential differenceappears across the output of the potentiometer?

3. If the arm moves through 10 degrees, by how much does the output of the potentiometer


change?

4. If the output of the potentiometer changes by 0.3 V through what angle has the arm turned?

Using a measurement amplifier as a comparatorQuestion 210S: Short Answer


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The illumination in an office should not fall below 400 lux. In order to save money a firm decides tocontrol the lights in the offices using a time switch and an electronic system which turns on the lightswhen the room is dimmer than the recommended value.

The system chosen uses a light dependent resistor (LDR), which monitors the light level in the office.At 400 lux the resistance of the light dependent resistor is 300 . If the light gets brighter itsresistance falls. If the light gets dimmer its resistance rises.

The light dependent resistor is connected in a potential divider in series with a 1.5 k resistanceacross a 9 V supply (of negligible internal resistance).

9 V

1.5 k

+

–

light dependent resistor

1. What is the potential difference across the light dependent resistor when the light level is 400 lux?


9 V

1.5 k

+

-

LDR

A B

1 k

5 k

2. A second potential divider with resistances of 5 k and 1 k is connected to the same supply.Show that the potential difference across the 1 k resistor is the same as that across the lightdependent resistor.

3. What is the potential difference between the terminals A and B in the circuit with two potentialdividers?

4. If the light gets dimmer, what will happen to the potential difference between terminals A and B?

5. A measurement amplifier is connected across the terminals A and B. It amplifies the differencebetween its inputs, and if its output is positive it turns the lights on.

9 V

1.5 k

+

-

LDR

A B

1 k

5 k

300

+

–output

measurementamplifier


Will the lights come on when the light in the office falls below 400 lux?

6. Modify the system to switch on a motor to close the window blinds if the light level exceeds 2000lux. The resistance of the light dependent resistor is 80 when the light level is 2000 lux.

Internal resistance of power suppliesQuestion 220S: Short Answer


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Answer the following questions for practice in making calculations about the internal resistance ofpower supplies.

Torch batteries, car batteries, EHT supplies and solar cells1. A typical hand-held torch runs off two 1.5 V cells, yet has a lamp rated at 2.5 V, 0.5 A. Explain

how the potential difference across the lamp can actually be 2.5 V as rated. What is the internalresistance of each cell, supposing them to be identical?

2. A typical car battery has an emf of 12 V, and must provide a current of 80 A to the starter motor.Why must the car battery have a very low internal resistance? If the internal resistance is 0.05 ,find the potential difference across this internal resistance when the starter motor is running. Whyis starting the car with the headlights on likely to affect their brightness?

3. Some school laboratories have EHT (Extra High Tension) power packs giving up to 3000 V. Forsafety, they are provided with a 50 M resistor in series with the supply. What is the maximumcurrent able to be drawn from the supply? Approximately what potential difference would there beacross a torch bulb connected across such a supply?

4. A student experimenting with a solar cell connects a 1000 voltmeter across it and observes apotential difference of 1.0 V. Using a different, extremely high resistance digital voltmeter, thereading is larger, 1.2 V. Why the difference? What is the internal resistance of the solar cell?


Resistance and conductance of thermistorsQuestion 250S: Short Answer


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Handling and plotting dataUse commercial thermistor data on a spreadsheet to make a variety of plots to see how theresistance and conductance of thermistors vary with temperature. It is this which allows thermistors tobe used as temperature sensors.

Data from RS Components Data Sheet 232-4538

Type Type Type Type Type

198-927 198-933 198-949 198-955 198-961

Temperature Resistance Resistance Resistance Resistance Resistance

T /°C R / k R / k R / k R / k R / k

-30 176.0 352.0 528.0 880.0 1760.0

-20 96.3 192.6 288.9 481.5 962.9

-10 54.9 109.7 164.3 274.3 548.5

0 32.4 64.8 97.2 162.1 324.1

10 19.8 39.6 59.4 99.0 198.0

20 12.5 24.9 37.4 62.4 124.7

25 10.0 20.0 30.0 50.0 100.0

30 8.07 16.13 24.20 40.33 80.66

40 5.34 10.68 16.03 26.71 53.42

50 3.62 7.24 10.85 18.09 36.18

60 2.50 5.00 7.51 12.51 25.02

70 1.76 3.53 5.29 8.82 17.63

80 1.27 2.53 3.80 6.33 12.65

90 0.923 1.845 2.768 4.613 9.226


Type Type Type Type Type

198-927 198-933 198-949 198-955 198-961

Temperature Resistance Resistance Resistance Resistance Resistance

T /°C R / k R / k R / k R / k R / k

100 0.683 1.367 2.050 3.417 6.834

110 0.516 1.032 1.547 2.579 5.158

120 0.394 0.788 1.183 1.971 3.942

130 0.305 0.610 0.914 1.524 3.048

140 0.238 0.476 0.715 1.191 2.382

150 0.188 0.376 0.564 0.941 1.881

160 0.150 0.299 0.449 0.748 1.495

170 0.120 0.241 0.361 0.602 1.204

180 0.0982 0.1964 0.2945 0.4909 0.9818

190 0.0809 0.1619 0.2428 0.4046 0.8093

200 0.0674 0.1348 0.2022 0.3370 0.6739

210 0.0567 0.1133 0.1700 0.2833 0.5665

220 0.0481 0.0961 0.1441 0.2403 0.4805

230 0.0411 0.0822 0.1233 0.2054 0.4109

240 0.0354 0.0708 0.1062 0.1770 0.3540

250 0.0307 0.0614 0.0922 0.15360.3072

Open the Excel Worksheet

How resistance and conductance vary with temperatureFirst, start up the spreadsheet of thermistor resistance data. It shows how the resistance, in k, offive different thermistors varies with temperature over the range –30 C to 250 C.

1. Scan the values in the table. What is the largest value of resistance in the table? What is thesmallest value of resistance in the table? What is that in ohm? What is the ratio of the largestresistance in the first column (type 198-927) to the smallest resistance in that column? Does thissuggest anything about how best to plot these data?

2. Use the spreadsheet graphing function to make an x-y plot of the resistance of the first thermistorlisted (type 198-927) against temperature in C. What does this graph show? Why is it almostuseless?


3. Now alter the resistance scale so that it is logarithmic. You can usually do this by clicking on they-scale on the graph, and selecting 'logarithmic' in the options for the y-scale. What do equalintervals on this new scale represent? How has the graph changed in appearance? What doesthe graph show?

4. Use the spreadsheet to calculate the ratio of the resistances of the thermistor (type 198-927) forsuccessive 10 degree intervals. (Be careful where there is an extra entry at 25 C.) What do yousee? Does this agree with the logarithmic graph?

5. Now make a combined plot, on a logarithmic resistance scale, showing how all five thermistorsbehave. What is remarkable about this plot? What does it mean?

6. This question is more difficult. What is the conductance in millisiemens of the thermistor type198-927 at 250 K when its resistance is 30.7 ? Predict the shape of the graph of conductanceagainst temperature. Use the spreadsheet to calculate the conductances of the thermistors overthe given temperature range, and make a logarithmic plot to check your prediction.

7 This question is even more difficult. There is in fact a straight line graph to be got from thethermistor data. It happens that to a good approximation the logarithm of the resistance (or of theconductance) of a thermistor is linearly related to 1 / T, the reciprocal of the absolute temperature.Use the spreadsheet to add 273 K to the temperatures given, to get the absolute temperature T,and then to calculate 1 / T for each value. A logarithmic plot of resistance or conductance against1 / T is a straight line.


Response time of thermistorsQuestion 260S: Short Answer


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The response time of a sensor or instruments will often seriously affect how well it works. Answerthese questions to test or develop your understanding of the idea.

Questions1. Which of the following is the best description of response time?

A The time it takes a sensor to start responding after a change in input

B The time from when a sensor starts responding to when it finishes

C The time from when the input changes to when the sensor completes responding

D The time it takes for a sensor to reach half of its final response

2. Three temperature sensors A, B and C were plunged into boiling water at the same momentwhen t = 0 s. The graph below shows their responses.

time / s

1.8

0 2

0.20.0

4 6 8 10

0.4

0.6

0.8

1.0

1.2

1.4

1.6 A

C

B

State the sensor with the longest response time

State the sensor with the shortest response time

State the sensor with the greatest sensitivity

State the sensor with the least sensitivity

State the response times of the three sensors A, B, and C

The temperature rise of each sensor was 80 ºC.

Calculate the average sensitivity of sensors A, B, and C between room and boiling watertemperatures, giving the correct units.


3. Two thermistors were plunged from cold water into boiling water and then back into the coldwater again. Each sensor was part of a potential divider circuit, also containing a fixed resistor.The output p.d.s of both circuits were datalogged as shown in the graph below.

Both thermistors decrease resistance with temperature. State and explain whether the output p.d.is taken across the fixed resistor or across the thermistor.


4. The main difference between the two thermistors is their physical size. The one giving rise to theblue data is a bead thermistor (about the size of a large pinhead); and the one giving rise to thered data is a barrel thermistor (about the size of a sugar cube). Explain the feature of the graphthat would have enabled you to deduce this fact without the legend labelling.

5. From the time axis deduce and state the time interval between data-logged samples. Hencededuce the response times for the two thermistors, blue and red.

6. Is there a significant difference in response times for warming and cooling of each thermistor?

7. What evidence is there that the boiling water is cooling during the first few minutes? State whichthermistor supplies this evidence and why the other one does not seem to provide evidence forthis.

8. Comment on the average sensitivities of the two thermistor circuits in the range from roomtemperature to near boiling.

Response time of light sensorsQuestion 270S: Short Answer


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Response time is an important concept with sensors and instruments of all kinds.

Questions1. Which of the following is the best description of response time?

A The time it takes a sensor to start responding after a change in input

B The time from when a sensor starts responding to when it finishes

C The time from when the input changes to when the sensor completes responding

D The time it takes for a sensor to reach half of its final response

2. Two light sensors were illuminated from a high power LED that was switched on/off by a signalgenerator on square wave output. The first sensor data (blue) was a slow LDR as part of apotential divider circuit, also containing a fixed resistor. The second sensor was a fasterphotodiode, giving rise to the red data, calibrated in lux. The outputs of both circuits weredata-logged as shown in the graph below, at two different frequencies of switching of the squarewave, at 1 Hz and 100 Hz nominal values from the signal generator.

The LDR decreases resistance with increasing light intensity. State and explain whether theoutput p.d. is taken across the fixed resistor or across the LDR.

3. State which graph you would use to estimate the response time of each sensor. Give yourreasons for this. Estimate the response times for the two light sensors. (Note that the units on thetime axis of the second graph are ms.)


4. Is there a significant difference in response times during brightening and darkening of each lightsensor?

5. Describe a problem with output from the LDR sensor circuit at the higher frequency of 100 Hz.State what you think the LDR circuit is sensing.

6. Calculate the percentage errors in the calibration of the signal generator against the moreaccurate clock of the data logger, using the following information taken from the graphs.

At nominal 1 Hz 1.1 oscillations last for 1.0 s;

At nominal 100 Hz 11 oscillations last for 102 ms.

Look closely at both data at the lower frequency. Describe and try to explain any anomalousbehaviour that you observe. (Look for evidence of noise in both signals, when they are notchanging very rapidly.)

7. Photodiodes cost about 10 times more than LDRs.

Give an example of an application where an LDR would be a perfectly adequate light sensor,explaining your reasoning.

Give an example of an application where an LDR would be an inadequate light sensor, and aphotodiode would be preferred, explaining your reasoning.


Baby, it's cold outside:The uses of sensors in the care of newborn babiesQuestion 10C: Comprehension


Quick Help

Looking after babies

Open the Adobe Acrobat PDF file

Source

Read the Science Museum pamphlet 'Baby, it's cold outside' which is about the design of incubatorsfor looking after newborn babies. Look carefully at the photograph of the incubator. Think about howthe baby's environment needs to be monitored. Think about how the baby itself needs to bemonitored. Find out what sensors are used.

What sensors?1. List the sensors used in the systems which control the baby's microenvironment (the incubator).

For each sensor, write down what is measured and where the sensor is placed.

2. List the sensors used to monitor the baby. What does each of them measure?

3. Nowadays the high technology systems for the care of babies are designed to be less stressful tothe baby than they used to be. How is this achieved?

4. A 'trigger ventilation' system is described. What characteristic does the sensor measure whichacts as the trigger?

Electron beamsQuestion 70C: Comprehension


Quick Help

Instructions Read the following passage before answering the questions that follow.

Cathode RaysGases are almost perfect insulators at small potential differences. But put the gas inside a sealedtube, lower its pressure and place a high potential between two electrodes and the gas will conduct! If


the p.d. is made high enough, the glass of the tube opposite the negative plate (the cathode)fluoresces, glowing green. If the positive electrode (the anode) is cut into a distinctive shape, ashadow of the same shape appears in the fluorescent glow. These observations led to the use of theterm 'cathode rays'.

positive anode

heatednegativecathode

electron beam

phosphor coating

shadow of cross

But what was the nature of this electricity? Hertz was convinced that there was electromagneticradiation coming off the cathode. British physicists including J J Thomson believed that there was astream of ions coming from the cathode or from the gas surrounding it. If the cathode stream wasreally made up of charged particles, an electrostatic force should deflect it. Experimentalists Hertzand Lenard, and then later Thomson himself, could not produce any deflection, and it looked as ifHertz' theory might be right.

cathode

anodewithslits

– +4 kVdeflecting platecan be made positive

deflecting platecan be made negative

cathode rays

gas at very low pressureionized in strong electric field

fluorescenceat tube end


In those days the tubes were evacuated by mercury pumps which were worked by hand and it tookhalf a day to remove enough gas to achieve a reasonably low pressure. Thomson decided that herewas where the problem lay; there was still too much gas in the tube. He finally succeeded in reducingthe pressure to a very low level indeed that allowed him to demonstrate that there were negativelycharged particles in the beam. J B Perrin provided confirmation that the charges were negative. Usinga magnet, he deflected the beam onto a gold leaf electroscope. He tested the collected charge andproved that it was negative.

collectingcan

electronbeamdeflected

heatingcircuit

4 kV

+–

gold leafelectroscope

Thomson measured the charge to mass ratio (e / m) of the particles in the cathode beam. He alsoexperimented with the charged particles given off from a white hot metal (thermionic emission) andthe particles produced when ultraviolet light strikes a metal surface. He found that the value of e / mwas the same for all these particles, at least within the limits of a large experimental error! The sameratio for positively charged H+ ions was already known from electrolysis experiments: it was 1000times smaller.

He announced his results at an evening meeting of the Royal Institution on April 30th 1897, saying

These numbers seem to favour the hypothesis that the carriers of the charges are smaller thanhydrogen atoms.'

Atoms are not indivisible, for electrified particles can be torn from them by the action of electricforces, the impact of rapidly moving atoms, ultraviolet light or heat.

He added in the Philosophical Magazine in the following October

The cathode-ray stuff weighed 1.3 10–8 g for every coulomb of electricity conveyed.

In the school laboratory, 'Teltron' tubes can be used to demonstrate the properties of electron beams.Electrons coming off the hot cathode are accelerated through a high p.d. before striking a screen. Thebeam current is about 2.0 mA at a p.d. of 5000 V.

Questions1. Find out the meanings of the terms: ion, fluorescence, thermionic emission.


2. The particles in the cathode rays transfer energy. Where does the energy of the particles gowhen they hit the end of the glass tube? (Use the first paragraph to help you.)

Hertz believed that cathode rays were electromagnetic radiation and would behave similarly to light.

3. What observation described in the passage supported his view?

4. Give two pieces of evidence (from the passage) to contradict his view.

Look at the diagram of the deflection tube.

5. How do you think Thomson demonstrated deflection by an electrostatic force?

6. Why are there slits in the anode?

7. How would you show that the particles are negatively charged?

8. In Perrin's experiment a magnetic field is used to deflect the beam of electrons into the collectingcan. What can you say about the direction of this magnetic field?

9. Use Thomson's figures to calculate the specific charge 'e/m' in SI units.

Now use the data on the Teltron tube from the last paragraph of the passage. You also need to knowthe charge on the electron e = 1.60 10–19 C and the specific charge 'e / m' = 1.76 1011 C kg–1.


10. Calculate the average kinetic energy gained by each electron.

11. Calculate the power dissipated at the screen.

12. Calculate the average number of electrons reaching the screen per second.

13. Calculate the speed of an electron just before it hits the anode.

14. What assumptions must you make for question 13?

15. Calculate the ratio of the calculated speed of the electron to the speed of light, c = 3.00 108 ms–1

.

Sensors and our sensesQuestion 80C: Comprehension


Quick Help

Read the following text and answer the questions at the end.

A continually humbling experience in the field of design is that despite enormous advances in areassuch as 'nanotechnology', we are still far from able to replicate designs which exist commonly innature. Many people in their professional and personal lives rely on air travel, yet we are unable torecreate the amazing efficiency of the flight of birds, their wing structure and response to climaticconditions. Bearable conditions in many of our homes rely on the pumps in air conditioning andcentral heating systems, but we are largely unable to copy the pumping action of the human heart.

It is possible to regard the quality of human experience as the sum of the output of a number ofprocessor units which 'sense' their environment and process the sensed information to formulate aresponse. In some cases this is automatic and easy to define: spinal reflexes will swiftly remove our


hand from a hot surface as a result of information sensed through the skin. More difficult to analyse isthe nature of perception whereby, for example, information heard from one source may provokedifferent responses to the same information heard from a different source. Imagine your own possiblerange of responses to being told how good you look today.

Can we compare our nervous systems with an electrical sensing and recording system? At firstglance, it may appear that there are similarities between an electrical sensor and a nerve cell. Asensor responds to stimuli and produces a signal; the dendrites of a nerve cell respond to stimuli andthe nerve cell produces a signal. The sensor is connected to a recording system by an electric circuit;a nerve cell is connected to other nerve cells by its axons; both transmit signals. The wires in anelectrical system will be insulated; the axon of a nerve cell may be insulated by a myelin sheath.

But here the similarities end. A wire may gain energy from the passage of an electric current throughit, whereas the propagation of impulses through a nerve cell is an active propagation process forwhich the cell has itself to use energy.

Questions1. List some similarities between the human nervous system and a system of electrical sensors

monitoring and controlling a process in a factory. Now list some differences.

2. Make a list of the different things your body can sense. For each, name, if possible, a type oflaboratory sensor which could do the same job.

3. The taste buds in our tongues produce signals in response to the presence of specific chemicalsubstances. What applications can you think of for electrical sensors which can signal thepresence of particular types of molecule?

4. List similarities and differences between your eye and an optical sensor such as alight-dependent resistor.

5. A constant source of speculation and interest is that of contact with 'alien' races. Much of thisspeculation assumes that aliens will be very similar to humans in their ability to sense theirenvironment. Imagine an alien race whose sensing systems are significantly different to our own.


Describe one or more of their sensing systems, and consider the problems of communicationbetween them and us.

Sensors and Formula 1 racingQuestion 90C: Comprehension


Quick Help

Thinking about sensorsRead the summarised article below, and look at the diagram showing the output of sensorsmonitoring the driver as he came near to crashing a Formula 1 car in wet conditions. Think about howthe different kinds of sensors might have worked.

My unforgettable one for the roadAdapted from an article in F1 Racing, by Tony Dodgins and Alan Copps.

Tony Dodgins writes:Tyrrell's regular driver, Mika Salo, paced about like some expectant father. He was worried about 'hisbaby' having all its limbs. The Finnish Formula 1 ace had been smart enough to negotiate one of the1995 cars for keeps at the end of its useful life. And now the car was out there on a drenchedBarcelona track in the hands of a journalist whose racing experience amounted to a season ofendurance Pro-Karting.

What you don't need with 700 brake horsepower is rain, but it was tipping down. Tough. The tracktime was non-negotiable. It was now or never. Plumes of spray fanned from the front tyres. Thesteering was direct, kart-like, but not heavy. Coming through on to Barcelona's mile-long straight forthe first time, I got on to the throttle and waited for the earth-shattering explosion of power. But itwasn't as dramatic as I'd thought. That was because they had programmed the electronic throttle fora delayed response and somewhat less than full power. I asked for more throttle and they gave mefull power. It was time for my last run.'

Leaving the pit lane I instantly felt the difference. I came out on the straight and gave it 85 percentthrottle. How did I know that? Because the ensuing 'moment' amused the team so much that theyexpanded it on the computer telemetry which monitors everything the car does. It's the ultimate spy inthe cab.

Instantly there was wheel spin, so I backed off, figuring the car must not have been straight.Convinced it now was, I gave it full throttle. Suddenly I was in a 1.5 G tail-slapper as the car snappedleft-right-left-right as quickly as you could blink. The Tyrrell crew ran for cover. 'The steering inputslooked mighty interesting and the wheel spin was off the graph!' an engineer explained later.


Engineer Alan Copps writes:You're never alone in a Formula 1 car. Every move made by the driver and every effect on the car ismonitored by sensors and stored in an on-board computer. During a race, this 'telemetry' istransmitted live to the pit engineers. The graph here shows what happened when Tony Dodginsmomentarily lost control.

4300 4350 4400 4450 4500 4550 4600 m

0

%

100

rawkph50

45

40

35

30

25

20

15

10

5

0

–5

–10

0

20

40

60

80

100

120bar

300

250

200

150

100

50

4

3

kph G's

2

1

0

–1

–2

–3

–40.0

A

C

Throttleposition

(raw) Lateralacceleration

(G-force)

B

Speed(kph)

Brake pressure(bar)

Wheelspin(kph)

13-113

Source

At point A on the graph, Dodgins put his foot down. The effect is seen on the line which shows the Gforces on the driver; a reading below zero is a force to the right, above to the left. From a steady levelclose to 1 G to the right going round a corner in the track, there is a quick shift to the left. The lineshowing wheel spin displays the difference in kilometres per hour between the speed of rotation ofthe rear powered wheels and that of the front wheels. That first touch on the throttle set the rearwheels spinning 7 kilometres per hour faster. The throttle then bounced as Dodgins tries to let the carsettle, and a moment later, at point B, he pressed the throttle to the floor. With 700 brake horsepowerblasting through the rear wheels, but with little adhesion in the wet conditions, the wheel spin went offthe graph. The speed rose to a peak close to 180 kilometres per hour. At point C, Dodgins lifted hisfoot, the right thing to do, but so violently that the wheels locked. The throttle responded instantly, andthe wheel spin graph shows the front wheels then turned faster. But the graph for brake pressure thenshows him doing, in the engineer's words, 'absolutely the wrong thing'. A stab on the brakes sent thecar's rear end slewing to the left, then to the right.

1. Look at the chart of the sensor outputs. Notice that the horizontal axis is distance in metres alongthe track, not time. Locate point A. At what distance along the track is this point? How couldDodgins have told from the graph that he 'gave it 85 percent throttle' at that moment? How far didthe car travel while the throttle was being increased from zero to 85 percent?


2. Between points A and C the speed rises rather steadily. By how much? What was the averagespeed during this time? Show that the car travelled about 100 m in this time. How long did thisacceleration last, in seconds? What was the acceleration, in m s–2? Comment on this value.

3. After point C the brakes come 'on' and the throttle is 'off'. Why does the speed not drop instantly?

4. Suppose you are in the engineering team designing sensors for a Formula 1 car. Suggest a kindof sensor that could be tried out, to detect: (i) throttle position, (ii) brake pressure, (iii) wheelspeed and (iv) lateral acceleration of driver (G force).

Lamp and resistor in seriesQuestion 190D: Data Handling


Quick Help

Study the characteristics of the two electrical components A and B shown.


0.5

0.4

0.3

0.2

0.1

00 3 6

potential difference / V

component B

component A

1. What is the resistance of each component with a potential difference of 3 V across it?

2. Suggest what each component could be.

The two components are connected in series across a variable d.c. supply of negligible internalresistance. A high resistance digital voltmeter measures the p.d. across A.

3. What is the current through A when the voltmeter reads 3 V?

4. What is the potential difference being provided by the supply?

5. If the supply potential difference is increased so that the voltmeter reads 6 V, what is the powerbeing dissipated in each component?

Using non-ohmic behaviourQuestion 270D: Data Handling


Quick Help

Instructions

Using a diode for meter protectionThe graphs show the characteristics of (i) a resistor made from a coiled wire and (ii) a diode (forwardbias).


0.5

0.4

0.3

0.2

0.1

00 10

p.d. / V

8642

1. Current - p.d. characteristic for wire coil

Use the characteristic for a wire coil.

1. Describe and account for the shape of the graph.

2. What is the resistance of the coil in the ohmic region?

3. Estimate the maximum electrical power rating of this resistance coil.

300

250

200

150

50

00 1.0

p.d. / V

0.80.60.40.2

2. Current - p.d. characteristic for diode

100


Use the characteristic for a diode

4. Describe and account for the shape of this graph.

5. Complete the table, using data from the graph to estimate the resistance of the diode in forwardbias, at different values of the potential difference.

Applied p.d./ V

0.50 0.55 0.60 0.65 0.70 0.75 0.80

Resistance /

The diode and the coil are connected in parallel across a variable d.c. source.

9 V

+

-

wire coil25

diode

6. Copy the characteristic of the coil in the range 0 to 0.8 V onto the diode characteristic above.Using a different colour draw a new curve to show how the total current supplied to the coilincreases as the applied p.d. increases from 0 to 0.8 V.


9 V

+

–

68

diode

mAmilliammeter 0-20 mA25

Some meters can be damaged if the current through them far exceeds the full scale current. Aschool physics technician is worried that the students may damage the milliammeters which theyhave been given to use in a circuit with a 68 resistor. These meters have a full scale deflectionof 20 mA, they have a resistance of 25 , and similar characteristics to those in the graph above.

The technician solders a diode in parallel with each meter.

7. Explain how this modification will protect the milliammeter.

Heating coilsQuestion 230X: Explanation–Exposition


Quick Help

Read the passage and think carefully about heating before answering the questions.

Heating elements can be made out of a coiled wire (e.g. manganin).

A student cuts 2 pieces of wire, 'A' to a length of 1 metre and 'B' to a length of 2 metres. She makeseach length into a small coil.

She is going to compare the rate of heating of the wires. She puts small equal volumes of cooking oilinto two insulated beakers provided with stirrers. She places one coil in each beaker and uses atemperature sensor connected to a datalogging package to monitor the rise in temperature.

In her first experiment she connects the coils in series across a suitable d.c. supply.

After letting the oil cool back down to room temperature she starts a second experiment, but this time


connects the coils in parallel to the same d.c. source.

1. Predict the ratio of the rates of heating of the oil produced by coil A to that produced by coil B foreach of the two experiments.

2. Each experiment is left running for 10 minutes. How do you think the final temperatures of the oilheated by coil A differ in the two experiments?

3. Suggest a reason why the ratios as measured would not agree exactly with your predictions.

Brightness of bulbsQuestion 240X: Explanation–Exposition


Quick Help

L

L

1

2

When two identical lamps are connected in series to a battery of negligible internal resistance theylight normally.

A variable resistor R is now connected across lamp L2. Explain what happens to the brightness ofeach bulb as the resistance of the variable resistor is:

1. Made low compared to the resistances of the lamps


2. Made high compared to the resistances of the lamps

Using a sensor in a potential dividerQuestion 260X: Explanation–Exposition


Quick Help

Cookie counterA cookie manufacturer wants to measure the production rate of the biscuits. Before the wrappingprocess, the biscuits will pass over a 'window' and block off light from a light dependent resistor(LDR).The LDR is connected into a potential divider arrangement, and the output voltage variationwith time will give the production rate.

The supply voltage will be 6 V and the load circuit will have a resistance of about 100 k.

1. Design a circuit which will give an output potential difference Vout > 4 V as the biscuit passes overthe window and Vout < 0.5 V when nothing obscures the window. The maximum possible current

permitted through the LDR is 20 mA. The resistance of the LDR in the dark is 10 M.


2. What effect if any will there be if the manufacturer decides to use a counter for the load circuitwhich has a resistance of 1 k?

Cut-off switchElectric kettles usually have an automatic switch which turns off the kettle when the water is boiling.

You have been asked to design a model of this device using an electronic switch which turns 'on' at0.6 V. You also have access to a fixed 6 V supply, a thermistor, a variable resistor and a number offixed resistors.

3. Draw a circuit diagram of your device, and give a brief explanation of how your device works.

4. If the thermistor has a resistance of 100 at 100 °C and 5000 at 20 °C, what value resistorshould you use?

Filament lamp and thermistor in seriesQuestion 280X: Explanation–Exposition


Quick Help

Before startingMake sure you are familiar with the characteristic graphs of the filament lamp and the thermistor.

Surge current protection1. Sketch graphs of current vs potential difference for a filament lamp rated 230 V; 25 W.

Explain the shape of the graph in terms of the effect of temperature on the conductance andresistance of the lamp.


2. Sketch graphs of current vs potential difference for a thermistor whose resistance decreases withtemperature.Explain the shape of the graph in terms of the effect of temperature on the conductance /resistance of the thermistor.

3. This circuit contains a filament lamp and thermistor in series with a 230 V supply. When theswitch is closed, the lamp glows dimly at first, but then gets brighter and brighter until the lamp islighting normally. Explain these observations.

230 V

thermistor

filament lamp

4. How does connecting a filament lamp in series with a thermistor protect the component from asurge current?

RobotsReading 10T: Text to Read

Teaching Notes | Key Terms

Quick Help


How can a robot see, touch or smell? What can robots do? What good or harm could they cause?This reading provides you with some information to use to think about such questions.

The idea of a robotThe name 'Robot' was first coined by Karel Capek, a Czech author, who wrote a play where peoplewere taken over by automatons looking like human beings. The Czech word 'robota' means work.

Robots have often starred in film and television. Some have been portrayed as humanoid and somenot. Some have been seen as friendly to humans, others as hostile and power seeking.

'Mechatronics', a word originating in Japan, first came into use in the 1970s. It is the integration ofmechanical and electronic principles together with computer technology for the intelligent control ofmachines. The 1980s saw the development of the microprocessor and other advances inmicroelectronics. In-built machine intelligence has numerous applications in new products: forexample a cooling fan using a microprocessor to vary the fan speed in relation to the ambienttemperature. This is an example of feedback in a system. However, even this modest level ofintelligence reduces the running cost and the noise level of the fan. Many rail systems such as theDocklands Light Railway, the Mass Rapid Transport System in Singapore are completely computercontrolled.

You might not describe your car as a robot, because at the moment people still do the driving!However, microprocessors inside control the ignition system, the cooling system, the flow of petroland can diagnose faults. Now that satellites in the Global Positioning System can tell your car where itis, and other satellites can monitor the road conditions, then with computerised route-finding you maysoon be driven by your own car.

We can program robots to carry out monotonous repetitive actions. For example, a robot arm with alaser cutting tool can cut out garments from 40 layers of fabric at a time for a clothing manufacturer.

Unpleasant or harmful environments do not affect them. Robots are used in industry forpaint-spraying and welding. The Fiat car production line is run by robots. Robots can safely handleradioactive materials; they do not need regular health checks or have to endure lengthy showers andscrubbing before going home! Robots can be used to carry out experiments in a hostile environment


such as Mars. They do not require a life supporting atmosphere.

To work, a robot needs three things: sensors to get information in; actuators (e.g. motors) to makemovements; and computing power to link information and action to the job in hand.

Thinking about robots Here are some things to think about.

1. Robots in films and television: are they believable? Do they have obvious sensors, actuators andmicroprocessors? Print out the picture of the robot and label parts of it with sensors and actuatorsit might need.

2. List jobs which automatic sensors already do in the home

3. What would be the problems of making a car that drives itself safely?

4. What is the effect on employment when robots enter the production line?

5. What tedious or dangerous jobs could be taken over by robots?

6. Discuss what a robot would need to do one of the following jobs:

artificial limbs: mimic the actions of the arm and hand

production lines: pick up a body panel, align its position and weld it into place.

pharmaceuticals: fill bottles with exact quantity required of radioactive tracer fordiagnosis, and pack in lead lined containers.

mail order: read computerised invoices, collect required number of specified items, carrythe to the loading bay and pack on the correct van for the required delivery area.

space station: make regular tests on the fabric of the station, check and maintain sealson doors and air locks etc.

housekeeping: do the dusting, vacuuming, making cups of tea, even tidying bedrooms

An electronic toaster which senses when the toast is doneReading 20T: Text to Read


Quick Help

The 'smart toaster' described here is a good but simple example of how electronic microsensors arebeing built into more and more consumer products, such as cars, washing machines and cookers.

A smart toaster

The productThe toaster is a consumer product with a very large market (in Europe alone some 20 million toasters


are sold every year). The bread is toasted in the toasters to a brown tan using heated resistive wiresclose to the slice. To attain the right colouring, the user has to set a timer to the estimated amount oftime needed to toast it just right. As blackened crusts all over the world testify, this is not always aneasy task. Braun AG in Germany has solved this problem in their infrared electronic-sensor toaster byconverting the toasting into a feedback process.

Source

Open the JPEG file

To control the toasting level, Braun uses an infrared sensor that measures the surface temperature ofthe bread slice by measuring the infrared radiation that it emits. The slice acts as an almost perfectblack body for the temperatures involved. At the predominant radiation in the wavelengths of 6.5 mto 14 m, almost all types of bread have an emissivity of approximately 0.98. Because the surfacetemperature of the bread slices during the toasting is a direct measure of the degree of toasting, agood toasting process can be implemented.

Only one significant problem had to be overcome: the red-hot heating wires close to the bread slicecan easily interfere with the measurement, since they emit much more radiation than the (relativelycold) bread slice. Therefore, a masking foil was placed between the sensor and the heating wires insuch a way that the sensor saw only the bread slice, and not the wires. Adding an infrared filterwindow to the sensor housing reduced the interference further. The filter transmits the radiationemitted by the slice at wavelengths of predominantly 6.5 m to 14 m, while reflecting the short-waveradiation of the red-hot heating wires.

sensor unit

infraredfilter

IR-sensor

slice of bread

masking foilinner toasterwall mica plate with

heater wires


The output signal from the sensor is amplified and fed into a control circuit. As soon as the requiredtoasting surface temperature has been achieved, the heating is turned off (without using the timercontrol). By setting a potentiometer, the set point of the control circuit can be adjusted to the desiredtoasting level (a nice golden tan for crispy slices, light brown if you want them toasted lightly or blackif you have just quarrelled with your partner).

The sensor for the applicationThe sensor used by Braun is a thin-film infrared sensor, made of a silicon-oxide / nitride membraneetched out of a silicon rim, with bismuth-antimony thermocouples to measure the temperaturedifference between the rim and the black absorbing area of 0.55 mm in diameter. The sensitive areaof the sensor has been blackened by evaporating a metal through a shadow mask (depositing aporous layer makes the metal very black). The specifications of the sensor are listed in the tablebelow.

Parameter Typical values Units

Size 3 3 mm2

Resistance 35 k

Output signal 2.5 mV

Responsivity 55 V W–1

Response time 25 ms

In high-volume consumer markets the parts have to be as inexpensive as possible. Therefore, thesensor chip should be as small as possible. The minimum size of a micro-machined chip is about 3mm by 3 mm. This is because the rim alone must be minimally 0.75 mm wide to allow for handling (itmust have a flat bottom of at least 400 m) and the lateral anisotropic etching (some 350 lam,depending on the wafer thickness). Consequently, a membrane of 1.5 mm by 1.5 mm requires a totalchip area of 3 mm by 3 mm.

The thermopile resistance is designed to be 35 k, which is a compromise between maximising thenumber of thermocouples and minimising the sensitivity to interference.

Source

Open the JPEG file

The amplification and control electronicsThe diagram below shows the toaster's electronic feedback system. The output signal of the sensor isamplified and then fed into a comparator, using a potentiometer (the toast adjustment knob on thetoaster) to weaken the amplifier output and obtain the desired degree of toasting. When thecomparator switches because the sensor output rises above the setting, the heating is turned off.

When there is no bread in the toaster, the sensor will see a heating wire on the opposite side of the


toaster, and its output signal will quickly rise. This is detected by the slice-detection circuit, which thendeactivates the comparator and sets the toaster to the baking mode, where the toaster is timercontrolled. The timer is set to a time interval optimised for baking bread rolls (on top of the toaster, notbetween the heater wires). After this interval the heater is switched off by the timer control.

amplifier comparator heaterswitch

safetyshutdown

slicedetection

circuit

infraredsensor

toastadjustment

timer

&

In addition to controlling the baking mode, the timer is used to switch off the toaster after a pre-setmaximum time interval in case the sensor control does not function properly. Thus, a safety shutdownensures that the toaster will not burn out.

DiscussionSensor-controlled toasting has several advantages over conventional time-controlled toasting: thesame degree of toasting is obtained each time, regardless of whether the bread is old, new or evenfrozen. It is also possible to heat up previously toasted slices without fatal burns.

By using a simple infrared-sensor detection scheme, the risky business of toasting a slice of bread isturned into a well-controlled process with reproducible results and greatly increased user-friendliness.Toasters with this infrared-sensor control are available at competitive prices, even though they are atthe top market level.

Interestingly enough, the sensor is about the most expensive part of the entire toaster. Therefore, alot of effort has been put into decreasing the cost of the infrared sensor, since the potential costreduction in the toaster is high. The price level of the infrared sensor has already been slashed to afew dollars.

Scaling-down arguments about why microchips run hotReading 40T: Text to Read


Quick Help

The arguments here link chapter 2 Sensing and chapter 4 Testing Materials, thinking about the powerdissipated in a circuit (chapter 2) and the resistivity or conductivity of a material (chapter 4).

Arguments about how quantities change when things are scaled up or down in size are common inphysics. This is an interesting example in which we see that the power dissipated in a circuit gets less


as the circuit is shrunk, but the power dissipated by a chip carrying many such circuits actuallyincreases.

Why microchips run hotIt seems obvious that, because in the microchip world resistances are large and currents are small,there will be no problem of chips getting hot. But this is wrong. This is because the energy has toescape from a much smaller surface area. Radiators to heat buildings are given as big a surface areaas possible. If they were smaller, they would have to be hotter to emit energy at the same rate. Soalthough small microchips have to get rid of less power, they have to do it from only a tiny area. Theyare liable to run hot, and so most computers need cooling fans.

This argument depends on three different ideas:

1. The potential difference involved does not change when a circuit is scaled down

2. The energy radiated or convected from a chip is proportional to its surface area

3. The conductance of a piece of material is proportional to its linear scale L, when it is scaled up ordown in the same proportions.

Here are arguments for each of these.

Potential difference does not scale downThe potential differences in, for example, a p-n junction depends on what the atoms, ions andelectrons in the material do. If it takes a certain energy to remove an electron from an atom on onescale, it takes the same energy to do the same on a smaller scale. The chip may be scaled down, butit's atoms are not.

Energy emitted is proportional to surface areaEnergy emitted from a solid object has to pass through its surface. If the energy is radiated, then abigger area provides more surface from which energy can be radiated. If the energy is convectedaway, air has to be blown over the surface and be warmed by it.

An object on a scale L has a surface area in proportion to L2.

Scaling down conductorsThe diagram below shows that if a bar of silicon carries current I with a potential difference V acrossit, then two such bars side by side will each carry current I . Combine them into one bar and thecurrent is 2I for the same potential difference V. That is:

Current is proportional to cross sectional area for a given potential difference


potential difference V

current I

current I

current I

current 2I

area A

area A

area A

Current increases with cross sectional area

If a potential difference V is enough to keep current I flowing along a bar, then if the current has to gothrough a second such bar, a further potential difference V is needed. Join the bars end to end andyou get a bar of twice the length, needing a potential difference of 2V to keep current I flowing.

Potential difference is proportional to length for a given current


Greater length needs greater potential difference




current I

current I

current I

potential difference 2V

length 2L

length L

current I

VG

difference potential

current = econductanc

I

Because the current I is in proportion to the cross sectional area A of a bar for a given p.d. V, theconductance G is proportional to area A.

However, as the potential difference V required for a given current I is larger the longer the length ofthe bar, the conductance G is inversely proportional to the length L .

Putting these together:

L

AG

length

area econductanc

L

AG

Thus if a silicon bar is scaled down by 1 / 1000, the area is scaled down by 1000 000 reducing theconductance by that factor. But the length is scaled down by 1000 which increases the conductanceby a factor 1000. Taken together the two changes reduce the conductance to 1 / 1000 of its formervalue.


Thus small things do not conduct as well as big things. An advantage is that insulating conductorsfrom one another on a microchip is not a problem.

Summary Let the linear dimensions of a circuit be L

conductance G of a conductor is proportional to L

resistance R of a conductor is proportional to 1 / L

If the potential difference V is the same then:

current I, proportional to G or to 1 / R is proportional to L

power dissipated I V is proportional to I and so to L

Thus, if L shrinks by 1000

the power dissipated by the conductor is 1000 times smaller

But more conductors can now be packed on the same area.

the area occupied by a circuit element is proportional to L2

the number of conductors on a given area is proportional to 1 / L2

Thus if L shrinks by 1000:

The number of conductors on a given area is 1000 000 times greater.

The power dissipated by each is 1000 times smaller.

Thus, the power dissipated in a given area is 1000 times greater.

This is the reason microchips often need cooling.

Kirchhoff's laws:Current and potential difference in complex circuitsReading 50T: Text to Read


Quick Help

You should already know how to calculate the resistance or conductance of resistors in series or inparallel (in series, add the resistances; in parallel add the conductances). But these rules are toolimited for use in general, when circuits may contain many components connected in a complicatedway. Kirchhoff's laws are simple, but provide a general way to analyse circuits of any complexity.

Kirchhoff's lawsGustav Kirchhoff (1824–1887) was a German physicist. He worked with Robert Bunsen on analysingthe spectra of elements – work for which the Bunsen burner was invented. He proposed that the dark


lines in the spectrum of the Sun, discovered by Joseph Fraunhofer, were caused by the absorption oflight in the atmosphere of the Sun, and so could be used to find out what elements there are in theSun.

Kirchhoff's name is given to two laws, formulated in 1845–6, which allow you to calculate the currentand potential difference anywhere in a complex network of components.

The two laws are:

1. At every junction in a circuit, the sum of the currents leaving the junction is equal to the sum of thecurrents entering the junction.

That is, electric charge is not created or destroyed, nor does it 'pile up' or 'get depleted' at a junction.In effect, this law says that electric charge is conserved and that the circuit is in a steady state.

2. Around any closed loop in a circuit, the sum of the potential differences across components iszero, if the loop contains no sources of emf, or is equal to the sum of the emfs around the loop.

This law says that energy is conserved. If there are no energy sources in a loop, the p.d.s must addup to zero, otherwise a charge could go round once, gain energy, go round again, gain energy again,and so on. If there are sources of energy, a charge going round the loop gains energy equal to thesum of that available from each source.

Example of the use of law 1

I1 I3 I5

I2 I4

E

In the top picture, Kirchhoff's first law says that:

0321 III

0543 III

Actually, there is no need to use these equations at all. The trick is to imagine a current flowing roundeach loop. The current in a component which belongs to two loops is the sum (noting the directions)of the two loop currents. The result of doing this is shown in the lower diagram. By putting in thecurrents in this way, Kirchhoff's first law is applied automatically.

Example of the use of law 2

E

IA IB IC

IA–IB IB– IC

To keep things simple, suppose all the resistors in the above diagram have the same resistance R.


In the left-hand loop, lower diagram, there is the emf E, and a p.d. across one resistor with a currentIA – IB through it. This gives the equation, for this loop:

)( BARE II (1)

In the central loop there are four resistors, and no source of emf. The equation is:

)()()()(0 BABCBB RRRR IIIIII or

ACB RRR III 40 (2)

Note that the last term is negative, because the loop is being traversed opposite to the currentdirection chosen.

In the right hand loop, there are again four resistors and no emf, giving:

)(0 CBCCC RRRR IIIII

or

BC RR II 40 (3)

From the last equation you can see that

CB II 4 (4)

Substituting for IC in equation (2) and dividing each term by R gives:

AB II 4

50

or

AB II5

4

(5)

Substituting for IB in equation (1) and dividing by R gives:

AAAR

EIII

5

1

5

4

or

R

EA 5I

(6)

Equation (6) now tells you IB at once:

R

EB 4I

(7)

And equation (4) tells you IC

, since BC II4

1 :

R

EC I

(8)


All the currents are now known, and any of the potential differences can be worked out if required.

SummaryUsing the 'loop current' method, you satisfy the first law automatically. Writing equations for the sumof the potential differences around each loop gives you as many equations as there are loops in thenetwork. These have to be solved as simultaneous equations.

When is a potential divider linear?Reading 70T: Text to Read


Quick Help

In general, the output of a potential divider is not proportional to the resistance of one of the tworesistors in the divider. This extension work shows how this arises, and indicates when a potentialdivider is a linear device.

Non-linear output of a potential dividerIn the diagram, a sensor with a resistance which changes is shown connected in a potential divider toa fixed resistance.

V

Rs Voutsensor

R

(R + Rs)I =

V

Vout = I Rs

= V Rs

(R + Rs)

Vout

V=

Rs

(R + Rs)

If the sensor resistance increases, the potential difference across it (the output of the potentialdivider) is the current multiplied by the sensor resistance. This is not proportional to the sensorresistance, because if that increases, the current decreases. Thus the output is the product of twofactors: sensor resistance and current. The result is that as the sensor resistance increases, the


output changes less and less for each equal increase in sensor resistance.

If you want a potential divider used like this to be as sensitive as possible, and to be approximatelylinear, then it is best to make the fixed resistance larger than the sensor resistance.

1.0

0.5

0

0 1 2 3 4 5

less sensitive regionoutput changes slowly with input

sensitiveregion

output changes rapidly with input

Rs = R

Vout

V(output)

Ratio Rs /R (input)

The spreadsheet model from which the results were calculated is provided.

Open the Excel Worksheet

Electronic noses: Telling fresh food from bad and detecting disease in cowsReading 80T: Text to Read


Quick Help

The reading is below gives details of an up-to-date method of using sensors to do what the humannose can do. It combines quite simple sensors, which detect gases by a change of electricalresistance, with clever analysis of data.

What is smell?What does the delicious smell of fresh coffee have to do with the need to change the diet of a herd ofcows? Both involve the human nose recognising a characteristic odour. In the case of the cows, a vet


can detect a disease called ketosis by smelling the cows' breath.

The distinctive smell of coffee does not come from one particular substance. In fact it comes fromhundreds of different molecules, each of which our noses can detect. The smell of coffee is a patternwe recognise. Our noses contain about a hundred million odour-sensitive nerve cells, whoseresponses to odour molecules are decided by about 1000 proteins which 'latch onto' odour moleculesdifferently. By processing the signals from these nerve cells, our brains identify a number ofcharacteristic smells, often at very low levels. For example you can detect the smell of bad fish at alevel of about 0.01 parts per billion.

Dairy cattle producing milk are prone to a condition called ketosis, which is due to inefficient digestionof the feed they are given. In this state, the cow's breath has a noticeable smell, part of which is dueto the presence of acetone (propanone). An experienced vet can detect the onset of the condition bysniffing the cow's breath. But the reliability with which this can be done varies between people anddepends on their own state of health. For this reason, engineers are trying to develop 'electronicnoses' which can automate the process. In a recent test, a system designed to detect ketosismanaged, in checks on 38 cows with and without ketosis, 8 out of 11 correct positive diagnoses, and26 out of 27 correct negative diagnoses. Not perfect, but getting there.

The food industry is interested in electronic noses, for monitoring the freshness of food. Recently atest car carried an electronic nose – which is still a bulky object, with all its electronics and controlhardware – around northern Italy to see how well it could sense motorway pollution.

How do electronic noses work?An electronic nose needs not one sensor for odour molecules in gases but, like the human nose,needs a whole array of sensors. Each sensor has to give a different response to a given combinationof molecules. One might give a big response to acetone but also to another molecule; another mightdo the same but be less sensitive to, say, acetone and more sensitive to yet another molecule. Thenthe signals from each sensor have to be compared, and patterns amongst them have to be identified.One successful experiment like this managed to distinguish between fresh ground coffee and instantcoffee, even telling two kinds of fresh ground coffee apart.

One way to detect patterns amongst signals is to feed them to a network of 'artificial neurons';electronic logic elements interconnected in a way which mimics on a small scale the interconnectionsbetween neurons in the brain. Such a network can be 'trained' to produce an output which appearsonly when a specific pattern is present in the input. Other ways include more traditional statisticalanalysis.

Sensors of several different types have been tried. One type uses metal oxides (for example tindioxide) whose resistance changes when the oxide adsorbs certain gases. These metal oxidesensors have to run hot (about 400 degrees Celsius) if they are to be sensitive enough and if they areto respond and recover rapidly enough. That makes demands on power, although the powerdemands of miniaturised sensors can be kept quite small. One commercially available electronic noseuses an array of up to 18 metal oxide sensors.

Another type of sensor uses electrically conducting polymers such as polypyrrole or polyaniline,which can work at room temperature. Polymers can be made whose electrical conductivity changesrapidly and reversibly in the presence of certain odours. It is thought that the odour molecules makethe polymer swell up, interfering with the mechanism of electrical conduction in them. They can detectodours down to 1 part per million or less. By choosing the right polymer, sensors can be built todetect rather specific odour molecules. In one experiment, an electronic nose using 20 conductingpolymer sensors coupled to a trained network of artificial neurons managed a 95% success rate indistinguishing the smells of lemon, roses, eucalyptus and banana.

Yet another type of sensor is of potential importance, because of the precision of measurement whichit potentially offers. Frequencies of oscillation can be measured extremely accurately, by electronic


counting and timing. The idea is to make a miniature oscillator out of quartz, which gives an electricalsignal when it is stretched or compressed (it is piezoelectric). Astonishingly, the presence of an odourcan be detected just through an increase in mass of the oscillator, which makes it oscillate lessrapidly. The increase in mass occurs when it collects some odour molecules on its surface. Thecapture of odour molecules is achieved by coating the quartz with a thin film of a substance (such asacetyl cellulose) which absorbs these molecules. Another similar kind of device makes waves, ratherlike earthquake waves, travel along a silicon surface, and measures their speed by using them tocreate oscillations. Again, when the surface absorbs molecules from above its mass increases. Thesurface film reduces the frequency of the waves by slowing them down.

What lies ahead?Electronic noses are a rapidly developing part of electronic engineering, combining ingenuity inmaking cheap, reliable and sensitive sensors, with the use of state of the art methods of data analysisincluding some which try to mimic how the brain works.

Some commercial systems exist, and a variety of industries are interested. But it will be some timebefore you can buy a nose to see if the food you have bought is fresh or not. And for the foreseeablefuture electronic noses will be specialised, built to detect a narrow range of odours for a specificapplication. The very sensitive general-purpose odour detector in the middle of your face willoutperform electronic noses for quite a time to come.

Find out about the Wheatstone bridgeReading 90T: Text to Read


Quick Help

This is material for further study, to interest you and extend your ideas. The Wheatstone bridge is aclever development of the idea of a potential divider.

The Wheatstone bridgeThe Wheatstone bridge circuit consists of two potential dividers arranged 'back to back'. Its output isthe difference between the outputs of the two potential dividers.

Wheatstone bridges are mostly used today in precision design of measuring instruments. Their greatadvantage is in eliminating unwanted signals whilst only retaining the required signal. They can bemanufactured quite easily on the microchip scale.

Charles Wheatstone (1802–1875) did not invent the Wheatstone bridge, which was the idea ofSamuel Christie (1784–1865). But he did much to popularise its use. His many inventions include anelectric telegraph, a kind of oscilloscope and devices for making stereoscopic images. He wasinterested in the physics of musical instruments and created the concertina. He was the first (1834) tomeasure the speed of an electrical signal along a wire.

Example: a precision load cellA load cell measures a force by bending or deflecting by a measurable amount when the force isapplied. The type shown here is fixed at one end and bent by a force applied at the other. Four straingauges, placed and connected as shown, are used in this carefully engineered design. The four


gauges are connected in a Wheatstone bridge circuit.

A strain gauge is a strip of metal foil, glued to the surface of the component whose strain is to bemonitored. The foil is stretched if the component is stretched. Any stretching along the length of thestrips in the foil is detected as an increase in resistance.

Professionally designed load cell

beam bends less herebeam bends more here

top surface stretched

lower surface compressed

straingauge effect amount temperature

stretched more

more

less

less

same

same

same

same

compressed

stretched

compressed

A

B

C

D

A

B

C

D

Vin

Vout

load

fixed end

A

B

C

D

The load cell shown above is designed to measure loads (forces) accurately, from the bending of thecarefully designed beam. The (white) internal cut-outs increase the bending for a given load. Theamount the beam bends is measured by the strain gauges A, B, C and D attached to the beam.

When the beam bends, gauge A's resistance goes up and gauge B's resistance goes down. GaugesC and D, fitted where the beam bends least, hardly change resistance. Each pair is connected in apotential divider. The two potential dividers are arranged 'back to back'; this circuit is called aWheatstone bridge. The output of the bridge is the difference between the output of the two potentialdividers.


beam bends most here beam bends least here

R + xR

R – xR

R

R

I = V

2RI = V

2RA

B

C

D

V

Wheatstone bridge as potential dividers back to back

VA =(1 + x) V

2

VB =(1 – x) V

2

output = VD – VB

= xV2

VC = IR =V2

VD = IR =V2

Approximations:Gauges A, B, C and D have equal resistance R, when the beam isnot loaded. The changes in resistance xR of A and B are equal andopposite. C and D do not change in resistance (first approximation)

How it works:When the beam bends, the output of the potential divider containinggauges A and B (VB ) changes by . The output of the potential dividercontaining gauges C and D (VD ) stays the same.

Result:The output from the bridge is the difference between the outputs ofthe two potential dividers

xV2

VD – VB = xV2

Think about the Wheatstone bridge as two potential dividers back to back. The output is thedifference between the outputs of the two dividers. A special case is shown: two gauges are affectedoppositely to one another; the other two are not affected at all.

The bridge has the added advantage that it compensates for changes of temperature. If all fourgauges suffer the same change in temperature then the bridge output is not affected. The bridgerejects the unwanted signal.

More subtly, by using four gauges, the bridge measures the difference between the bending where Aand B are placed from that for C and D. The difference between the bending at these two places isnot much affected by just where the load is applied.

The Wheatstone bridge was invented for accurate comparisons of resistances. Today its use is moreoften in designs like that of the load cell. In these designs, the four resistances are generally equal,and the output measures changes in them.

Help with calculating current and power in an ion beamReading 30S: Text to Study


Teaching Notes | Key Terms Quick Help

These notes aim to help you to see how to calculate the rate of flow of charge and the rate at whichenergy is delivered, by a beam of moving charged particles.

Calculating the currentRail trucks carry coal, and the coal carries energy. Ions carry electric charge and their charges carryenergy. So you can think about a beam of moving charged particles as being like a train of coal trucksall moving together.

Question: A coal truck carries 2 tonnes of coal. A train of 100 coal trucks takes a total time of 5minutes to pass you. How much coal passes you each minute?

Answer: 20 coal trucks pass you in one minute (100 in 5 minutes). Each carries 2 tonnes of coal. So40 tonnes of coal pass you per minute. If the train arrives at a power station, 40 tonnes of coal aredelivered per minute.

The calculation can be written as an equation:

Rate of flow of coal ('coal current') = coal carriers per second coal in each carrier

Question: An ion carries 1.6 10–19 coulombs of electric charge. 1021 ions pass you in 100 seconds.How much electric charge passes you per second? What is the electric current in amperes?

Answer: If 1021 ions pass in 100 seconds then 1019 ions pass in 1 second (1021 / 102 = 1021– 2 = 1019

). The electric charge passing per second is the number of ions passing per second multiplied by theelectric charge on each ion. Thus the electric current (charge per second) is 1.6 10–19 1019 = 1.6coulombs per second, or 1.6 amperes.


Rate of flow of charge (electric current) = charge carriers per second charge on each carrier

Calculating the powerCoal is delivered to power stations because it carries energy (if there is oxygen to burn it with). Thepower provided to the power station is the amount of energy provided per second.

Question: A conveyer belt carries powdered coal to the furnace of a power station. The belt delivers30 kg of coal every minute. One kilogram of coal provides 30 MJ of energy. What is the powerdelivered to the furnace?

Answer: The rate of flow of coal is 30 kg every 60 seconds, which is 0.5 kg per second. 1 kg of coalcarries 30 MJ so 0.5 kg carries 15 MJ of energy. Thus the rate of delivery of energy, or power, is 15MJ per second, or 15 MW, or 15 106 W.


Rate of flow of energy (power) = rate of flow of coal in kg s–1 energy carried by coal in J kg–1

Question: A beam of ions has been accelerated by a potential difference of 1000 volts. The beamcurrent is 10 milliamperes. What power does the beam deliver?

Answer: The potential difference is the energy given to each coulomb of charge. From a potentialdifference of 1000 volts, one coulomb of charge would have an energy of 1000 joules.

A current of 10 milliamperes, or 10–2 A, delivers 10–2 coulombs per second. If each coulomb carries


1000 joules, the power delivered is 1000 10–2 joules per second, that is 10 watts.


Rate of flow of energy (power) = rate of flow of charge in C s–1 energy carried by charge in J C–1

= electric current in A potential difference in V.

The potential divider in picturesReading 60S: Text to Study


Quick Help

It is helpful to see a visual image of how the potential divider works, when connected up with resistorswhich are equal or not, and which have various values of their resistance.

The potential divider in picturesHere are five diagrams of a potential divider.


much morethan V/2

much lessthan V/2

V V VV/2 V/2 V/2

V V

Equal resistances

Unequal resistances

The potential divider in pictures

resistance potentialdifference

current

Key

All are connected to the same input potential difference V.

The top row of three diagrams shows potential dividers with pairs of equal resistances. In one casethe two resistances are both middling in value and in the other two cases they are both high in valueor low in value. The output of all three potential dividers is the same, half the input potentialdifference, or V / 2. How does this come about? When the resistances are low, the current is high.When the resistances are high, the current is low. The product of current and resistance, the potentialdifference I R is the same.

The bottom two diagrams show potential dividers made with one high value and one low valueresistance. The sum of the two is a middling resistance, so the current is middling in size. Thepotential difference I R across the high value resistance is large; the potential difference across thelow value resistance is low.

The output depends on which way round the resistances are connected. If the output is taken acrossthe high value resistance, it is high, larger than V / 2. If the output is taken across the low valueresistance, it is low, less than V / 2.


Revision Checklist I can show my understanding of effects, ideas and relationships bydescribing and explaining:how electric currents are a flow of charged particles e.g. an electron beam in a TV tube, electrons in a metal, electrons and holes ina semiconductor

A–Z references: electric current, electron beam

the idea of potential difference in an electric circuit, as energy per unit charge

A–Z references: potential difference

Summary diagrams: Rivers and electric currents

what resistance and conductance mean

A–Z references: conductance, resistance

what happens to potential difference and current in circuits with componentsconnected in series and in parallel using the ideas of resistance andconductance as appropriate

A–Z references: parallel circuit, series circuit

Summary diagrams: Conductors in parallel and series, Series and parallel rivers

what electromotive force (emf) means

A–Z references: electromotive force, see also potential difference

what is meant by internal resistance and the effect of internal resistance in acircuit

A–Z references: internal resistance

Summary diagrams: Sources and internal resistance

the idea of power in electric circuits as energy dissipated or transferred persecond

A–Z references: electrical power

the relation between current and potential difference in ohmic resistors i.e. resistors which follow Ohm's law so that the ratio V / I stays the same whenexternal conditions (such as temperature) stay the same

A–Z references: Ohm's law, non-ohmic conductors

the action of a potential dividere g in sensor applications such as to sense position or angle reduce a


e.g. in sensor applications such as to sense position or angle, reduce apotential difference, produce a potential difference from a change in resistance

A–Z references: potential divider

I can use the following words and phrases accurately:with reference to electric circuits: emf, potential difference, current, charge,resistance, conductance, series, parallel, internal resistance, load

A–Z references: electric current, potential difference, conductance, resistance,parallel circuit, series circuit, electromotive force, internal resistance

with reference to instrumentation: resolution, sensitivity, stability, response time,calibration, systematic error, zero error

A–Z references: resolution, sensitivity, response time, systematic error, randomuncertainty

I can sketch and interpret:simple circuit diagrams

A–Z references: parallel circuit, series circuit, potential divider

graphs of current against potential difference; graphs of resistance orconductance against temperature

A–Z references: Ohm's law, non-ohmic conductors

I can calculate:the conductance G of a circuit or a component using the relationship G = I / Vand rearrange the equation to calculate other quantities


the resistance R of a circuit or a component using the relationship R = V / I andrearrange the equation to calculate other quantities


charge flow in a circuit or component using the relationships Q = I t, Q = W / Vand rearrange the equations to calculate other quantities

A–Z references: electric current, potential difference, electrical power

current, circuit resistance and potential differences in series circuits using theresistances of componentse.g. total resistance = sum of component resistances

A–Z references: conductance, resistance, series circuit

currents, circuit resistance and potential differences in parallel circuits using the


currents, circuit resistance and potential differences in parallel circuits using theconductances of componentse.g. total conductance = sum of component conductances

A–Z references: conductance, resistance, parallel circuit

the power dissipated in a circuit using the relationship P = I V and rearrange theequation to calculate other quantities


power, current, resistance and potential difference in circuits and components

using the relationships P = I 2R, P = V2 / R and rearrange the equations tocalculate other quantities


energy dissipated in a circuit W = V I t


current, potential difference and resistance in circuits with internal resistance,e.g. using the relationships V = – I r internal and V = I Rload and rearrange theformulae to calculate other quantities

A–Z references: potential difference, electromotive force, internal resistance

the effects produced by potential dividers in a circuite.g. when an LDR or thermistor is used in a sensing application

A–Z references: potential divider

I can show my ability to make better measurements by:identifying and estimating the largest source of uncertainty in measurementswith sensors and electrical instruments

A–Z references: accuracy, uncertainty

taking account of properties of sensors and instruments: resolution, sensitivity,stability, response time, and calibration, systematic and zero error

A–Z references: resolution, sensitivity, response time, calibration, uncertainty,systematic error

using dot-plots or histograms of repeated measurements to estimate mean andrange of values, and identify possible outliers

A–Z references: random uncertainty, uncertainty

plotting graphs including uncertainty bars, using them to estimate uncertainty ingradient or intercept

A–Z references: uncertainty, graphs

considering ways to reduce the largest source of uncertainty in an experiment


A–Z references: accuracy, uncertainty

I can show an appreciation of the growth and use of scientificknowledge:giving examples of and commenting on the applications of sensors

A–Z references: sensor

Documents

Advancing Physics Chapter 2