Electricity and Fields Questions

8 (Question B1 continued) Current electricity

M04/431/H(2)

A cell of electromotive force (e.m.f.) E and internal resistance r is connected in series with a resistor R, as shown below.

E

r

R

The cell supplies 8.1103 of energy when 5.8 103 J C circuit. The current in the circuit is constant. (c) (i) Calculate the e.m.f. E of the cell.

of charge moves completely round the

[2]

..................................................................... ..................................................................... ..................................................................... (ii) The resistor R has resistance 6.0 . The potential difference between its terminals is 1.2 V. Determine the internal resistance r of the cell. ..................................................................... ..................................................................... ..................................................................... ..................................................................... (iii) Calculate the total energy transfer in the resistor R. ..................................................................... ..................................................................... ..................................................................... [2]

[3]

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9 (Question B1 continued)

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(iv) Describe, in terms of a simple model of electrical conduction, the mechanism by which the energy transfer in the resistor R takes place. ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... .....................................................................

[5]


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2 SECTION A Answer all the questions in the spaces provided.

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A1. Data based question. This question is about change of electrical resistance with temperature. The table below gives values of the resistance R of an electrical component for different values of its temperature T. (Uncertainties in measurement are not shown.) T/ C R/ (a) R. 1.2 3590 2.0 3480 3.5 3250 5.2 3060 6.8 2880 8.1 2770 9.6 2650

On the grid below, plot a graph to show the variation with temperature T of the resistance [3] Show values on the temperature axis from T = 0C

to T = 10

C

.


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3 (Question A1 continued) (b) (i)

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Draw a curve that best fits the points you have plotted. Extend your curve to cover the temperature range from 0 C to 10 C . Use your graph to determine the resistance at 0 C and at 10 C Resistance at 0 C = . . . . . . . . . . . . . . . . . . . . . . . Resistance at 10 C = . . . . . . . . . . . . . . . . . . . . . .

[1] [2]

(ii) .

(c) C

On your graph, draw a straight-line between the resistance values at 0 line shows the variation with temperature (between assuming a linear change. 0 C an d

and at 10 C . This [1]

10 C ) of the resistance,

(d)

(i)

Assuming a linear change of resistance with temperature, use your graph to determine the temperature at which the resistance is 3060 . Temperature = . . . . . . . . . . . . . . . . . . . . . . . . . . C

[1]

(ii)

Use your answer in (d)(i) to calculate the percentage difference in the temperature for a resistance of 3060 that results from assuming a linear change rather than the non-linear change. ..................................................................... ..................................................................... .....................................................................

[3]

(e)

In a particular experiment to measure the variation with temperature of the resistance, each measurement of resistance has an uncertainty of ! 30 and the uncertainty in the C . temperature measurements is ! 0.2 (i) On your graph in (a), show the uncertainties in the values of R and of T for temperatures of 1.2 C, 5.2 C and 9.6 C . State and explain whether, within the experimental uncertainties, the relationship between resistance and temperature could be linear. ..................................................................... ..................................................................... .....................................................................

[2]

(ii)

[2]

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6 A3. This question is about a filament lamp. (a)

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On the axes below, draw a sketch-graph to show the variation with potential difference V of the current I in a typical filament lamp (the IV characteristic). (Note: this is a sketchgraph; you do not need to add any values to the axes).

[1]

V

0 (b) (i)

0

I [1]

Explain how the resistance of the filament is determined from the graph. ..................................................................... .....................................................................

(ii)

Explain whether the graph you have sketched indicates ohmic behaviour or nonohmic behaviour. ..................................................................... .....................................................................

[1]

A filament lamp operates at maximum brightness when connected to a 6.0 V supply. At maximum brightness, the current in the filament is 120 mA. (c) (i) Calculate the resistance of the filament when it is operating at maximum brightness. ..................................................................... (ii) You have available a 24 V supply and a collection of resistors of a suitable power rating and with different values of resistance. Calculate the resistance of the resistor that is required to be connected in series with the supply such that the voltage across the filament lamp will be 6.0 V. ..................................................................... ..................................................................... ..................................................................... [1]

[2]

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14 (Question B1 continued) part 2 Heating water electrically

M06/4/PHYSI/HP2/ENG/TZ1/XX+

The diagram below shows part of the heating circuit of a domestic shower. insulated wire 240 V supply water pipe

cold water 14 C insulated heating element

hot water 40 C

Cold water enters the shower unit and flows over an insulated heating element. The heating element is rated at 7.2 kW, 240 V. The water enters at a temperature of 14 C and leaves at a 3 1 1 temperature of 40 C. The specific heat capacity of water is 4.210 J kg K . (a) Describe how thermal energy is transferred from the heating element to the water. ...................................................................... . ...................................................................... . ...................................................................... . ...................................................................... . ...................................................................... . (b) Estimate the flow rate in kg s of the water. ....................................................................... ....................................................................... ....................................................................... ....................................................................... ....................................................................... .......................................................................1

[3]

[4]


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15 (Question B1, part 2 continued) (c)


Suggest two reasons why your answer to (b) is only an estimate. 1. .................................................................. .................................................................. 2. .................................................................. ..................................................................

[2]

(d)

Calculate the current in the heating element when the element is operating at 7.2 kW. ....................................................................... ....................................................................... .......................................................................

[2]

(e)

Explain why, when the shower unit is switched on, the initial current in the heating element is greater than the current calculated in (d). ....................................................................... ....................................................................... .......................................................................

[2]


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16 (Question B1, part 2 continued) (f)


In some countries, shower units are operated from a 110 V supply. A heating element operating with a 240 V supply has resistance R240 and an element operating from a 110 V supply has resistance R110. (i) Deduce, that for heating elements to have identical power outputs R110 R240 = 0.21. [3]

.................................................................. .................................................................. .................................................................. .................................................................. .................................................................. .................................................................. .................................................................. .................................................................. (ii) Using the ratio in (i), describe and explain one disadvantage of using a 110 V supply for domestic purposes. .................................................................. .................................................................. .................................................................. ..................................................................

[2]

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8 a3. This question is about an electric circuit.


A particular filament lamp is rated at 12 V, 6.0 mA. It just lights when the potential difference across the filament is 6.0 V. A student sets up a electric circuit to measure the I-V characteristics of the filament lamp. In the circuit, shown below, the student has connected the voltmeter and the ammeter into the circuit incorrectly. A

12 V

S

100 k V

The battery has e.m.f. 12 V and negligible internal resistance. resistance and the resistance of the voltmeter is 100 k. The maximum resistance of the variable resistor is 15 . (a)

The ammeter has negligible

Explain, without doing any calculations, whether there is a position of the slider S at which the lamp will be lit. ....................................................................... ....................................................................... ....................................................................... ....................................................................... .......................................................................

[3]

(b)

Estimate the maximum reading of the ammeter. ....................................................................... .......................................................................

[2]


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9 (Question A3 continued) (c)


Complete the circuit diagram below showing the correct position of the voltmeter and of the ammeter in order to determine the I-V characteristics of the filament lamp.

[2]

12 V

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21 b3.


This question is about electric current and the effects of electric current. Electric current (a) The diagram below shows the circuit used to measure the current-voltage (I-V) characteristic of an electrical component X.

X

On the diagram above, (i) (ii) label the ammeter A and the voltmeter V. mark the position of the contact of the potentiometer that will produce a reading of zero on the voltmeter. Label this position P. [1 ] [1 ]


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22 (Question B3 continued) (b)


The graph below shows the current-voltage (I-V) characteristics of two different conductors X and Y.

0.50 0.45 0.40 0.35 0.30 0.25 I/ A 0.20 0.15 0.10 0.05 0.00 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 V/V (i) State the value of the current for which the resistance of X is the same as the resistance of Y and determine the value of this resistance. Current: ........................................................ Y X

[2]

Resistance: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ........................................................ (ii) Y. Describe and suggest an explanation for the I-V characteristic of conductor .................................................................. .................................................................. .................................................................. .................................................................. .................................................................. (This question continues on the following page)2206-6514

[3]

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23 (Question B3 continued) (c)


The two conductors X and Y are connected in the circuit as shown below.

12 V

Z X

Y The cell has e.m.f. 12 V and negligible internal resistance. The resistor Z has resistance R and the potential difference across the conductors X and Y is 5.0 V. (i) Use the graph in (b) to determine the total current in the circuit. ................................................................. . ................................................................. . ................................................................. . (ii) Determine the resistance R of the resistor Z. .................................................................. .................................................................. .................................................................. .................................................................. (iii) Determine the total resistance of the parallel combination of X and Y. .................................................................. .................................................................. .................................................................. .................................................................. [2] [2] [2]

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26 b3.


This question is in two parts. part 1 is about electrical conduction and part 2 is about thermodynamics. part 1 Electrical conduction

In a copper wire the number of conduction electrons is equal to the number of copper atoms in the wire. (a) State what is meant by conduction electrons. ....................................................................... ....................................................................... (b) (i) The density of copper is 8.93 10 kg m and its molar mass is 64 g. Deduce 3 5 that the number of moles of copper in a volume of 1.0 m is 1.4 10 . .................................................................. .................................................................. .................................................................. (ii) Estimate the number of conduction electrons in 1.0 m of copper. .................................................................. .................................................................. (c) The diagram below shows some of the conduction electrons in a copper wire. The arrows represent the random velocities of some of the electrons.3 3 3

[1]

[2]

[1]

copper wire Explain, by reference to the motion of the electrons, why there is no current in the wire. ....................................................................... ....................................................................... [2]


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27 (Question B3, part 1 continued) (d)


An electric field is established inside the copper wire directed as shown in the diagram below. The dots represent electrons. The random velocities of the electrons are not shown. On the diagram below, draw an arrow to indicate the direction of the drift velocity of the electrons.

[1]

electric field

copper wire (This question continues on the following page)

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28 (Question B3, part 1 continued) (e)


A typical value for the electron drift velocity in a copper wire is 10 m s . In the circuit below, the length of the copper wire joining the negative terminal of the battery to the lamp is 0.50 m. S

3

1

0.50 m

(i)

The switch S is closed. Calculate the time it would take for an electron to move from the negative terminal of the battery to the lamp. ..................................................................

[1]

(ii)

The lamp lights in a time much less than that calculated in (e)(i). Explain this observation. .................................................................. .................................................................. .................................................................. ..................................................................

[2]

(iii) Discuss, in terms of the movement of the electrons, the energy transformations taking place in the filament of the lamp. .................................................................. .................................................................. .................................................................. .................................................................. .................................................................. ..................................................................

[4]


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29

M07/4/PHYSI/HP2/ENG/TZ1/XX+ (Question B3, part 1 continued) (f) The diagram below shows part of a circuit that may be used to determine the current - potential difference (I-V) characteristics of a lamp.

An ammeter and a voltmeter are required. On the diagram above, draw symbols to show the correct positions of the ammeter and the voltmeter. [2] (g)I / A 0.50 0.40 0.30 0.20 0.10 0.00 0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 V/V

The I-V characteristics for one lamp are shown below.

(i)

State a range of values of the current I for which the lamp may be considered to show ohmic behaviour. ..................................................................

[1]

(ii)

The potential difference across the lamp is 0.80 V. Calculate the resistance of the lamp at this potential difference. .................................................................. ..................................................................

[2]

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6 a2. This question is about electric circuits. (a) Define e.m.f. and state Ohms law. e.m.f.:


[2]

........................................................... ...........................................................

Ohms law:

........................................................... ...........................................................

(b)

In the circuit below an electrical device (load) is connected in series with a cell of e.m.f. 2.5 V and internal resistance r. The current I in the circuit is 0.10 A. e.m.f. = 2.5 V

r I = 0.10 A load The power dissipated in the load is 0.23 W. Calculate (i) the total power of the cell. .................................................................. .................................................................. (ii) the resistance of the load. .................................................................. .................................................................. .................................................................. .................................................................. (iii) the internal resistance r of the cell. .................................................................. .................................................................. .................................................................. .................................................................. (This question continues on the following page)2207-6514

[1]

[2]

[2]

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A second identical cell is connected into the circuit in (b) as shown below.

I = 0.15 A load

The current in this circuit is 0.15 A. Deduce that the load is a non-ohmic device. ....................................................................... ....................................................................... ....................................................................... ....................................................................... ....................................................................... .......................................................................

[4]

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from the proton. .................................................................. 22 M08/4/PHYSI/HP2/ENG/TZ1/XX+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . electric . . . and . . . . . . . . . . . b3. . .This.question .is in.two .parts. .Part 1 is.about.aspects.of . . . . . .fields . . . electric charge. and . . . . Part 2 is about thermodynamics. .................................................................. Part 1 Fields and electric charge associated with atoms .................................................................. (a) A proton may be considered to be a point charge. For such a proton (i) sketch the electric field pattern. [2]

(ii)

calculate the magnitude of the electric field strength at a distance of 5.0 1011 m

[2]


(i) Using your answer to (a)(ii) deduce that the magnitude of the electric force between the electron and the proton is . *10?8 N.2208-6508

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M08/4/PHYSI/HP2/ENG/TZ1/XX+ (ii) (Question B3, part 1 continued) Deduce that the kinetic energy of the electron is 2. *10 ?18 J. (b) In a simple model of the hydrogen atom, an electron orbits the proton. Both electron and proton are regarded as point charges. The orbital radius of the electron is 5.0 1011 m .

2

..................................................................

[1]

..................................................................

[3]

..................................................................

.................................................................. (c) The electron in (b) also has electrostatic potential energy.

. . . . . . . . . (i). . .Define electrostatic . . . . . . . . a point. . . . . . . . . . . . . . . . . . . . . . . . . . . . . [2] . . . . . . . . . . . . . potential at . . . . . .................................................................. .................................................................. .................................................................. (ii) Calculate the electrostatic potential energy of this electron. .................................................................. .................................................................. .................................................................. .................................................................. [2]


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24 (Question B3 part 1 continued) (d)


Using your answers in (b)(ii) and (c)(ii) determine the energy required, in electron volt, to completely remove the electron from the influence of the proton. ....................................................................... ....................................................................... ....................................................................... .......................................................................

[2]

Fields and electric charge in conductors (e) Define electromotive force (e.m.f.). ....................................................................... ....................................................................... (f) A filament lamp is operating at normal brightness. The potential difference across the lamp is 6.0 V. The current in the filament is 0.20 A. For the filament of this lamp, calculate (i) the resistance. .................................................................. .................................................................. [1] [1]

(ii)

the power dissipated. .................................................................. ..................................................................

[1]


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25 (Question B3 part 1 continued) (g)


The lamp in (f) is connected in the circuit below. The lamp is still operating at normal brightness.

B

R

The battery B has an internal resistance of 5.0 and the resistance R of the resistor 15 . (i) Calculate the current in the resistor R. .................................................................. .................................................................. [1]

(ii)

Determine the e.m.f. of the battery. .................................................................. .................................................................. .................................................................. .................................................................. .................................................................. ..................................................................

[4]


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11 SECTION B

N05/4/PHYSI/HP2/ENG/TZ0/XX+

This section consists of four questions: B1, B2, B3 and B4. Answer two questions. B1. This question is in two parts. Part 1 is about electrical circuits and Part 2 is about the physics of cooling. Part 1 Electrical circuits Andrew is set the task of measuring the current-voltage (I-V) characteristics of a filament lamp. The following equipment and information are available. Information Battery Filament lamp Voltmeter Ammeter Potentiometer (a) e.m.f. = 3.0 V, negligible internal resistance marked 3 V, 0.2 A resistance = 30 k, reads values between 0.0 and 3.0 V resistance = 0.1 , reads values between 0.0 and 0.5 A resistance = 100

For the filament lamp operating at normal brightness, calculate (i) its resistance. ................................................................ . ................................................................ . (ii) its power dissipation. ................................................................ . ................................................................ . [1] [1]


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12 (Question B1, part 1 continued) Andrew sets up the following incorrect circuit.


V

A

(b)

(i)

Explain why the lamp will not light. ................................................................ . ................................................................ . ................................................................ .

[2]

(ii)

State the approximate reading on the voltmeter. Explain your answer. ................................................................. ................................................................. .................................................................

[2]

(c)

On the circuit diagram below, add circuit symbols to show the correct position of the ammeter and of the voltmeter in order to measure the I-V characteristics of the lamp. [2]


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13 (Question B1, part 1 continued) (d)


On the axes below draw a sketch graph to show the I-V characteristics for this filament lamp. [4] I/A 0.3

0.2

0.1

0.0 0.0 (e) 1.0 2.0 3.0 4.0 V/V [2 ]

Explain the shape of the graph that you have drawn in (d). ...................................................................... ...................................................................... ...................................................................... ......................................................................


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8 a3. This question is about electrical circuits.

N07/4/PHYSI/HP2/ENG/TZ0/XX

The graph below shows the I-V (current-voltage) characteristic of an electrical component T. 150

100

I / mA

50

0 0.0

2.0

4.0 V/V

6.0

8.0

(a)

On the graph above, draw the I-V characteristic in the range V 0 to V 6.0V for a resistor R having a constant resistance of 40 . [1]


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9 (Question A3 continued) (b)


The component T and the resistor R are connected in parallel as shown below. T

R 40 A B

When a battery of constant e.m.f. E and negligible internal resistance is connected between the terminals A and B, the current in the resistor R is 100 mA. (i) Calculate the e.m.f. E of the battery. .................................................................. .................................................................. (ii) Use the graph to determine the current in T. .................................................................. (iii) Calculate the power dissipation in T. .................................................................. .................................................................. .................................................................. [2] [1] [1]


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In order to reduce the power dissipation in component T, a second resistor R of resistance 40 is connected in series with T. The circuit is shown below. T R 40 R 40

A The battery connected between A and B is unchanged. Use the graph to determine (i) the current in resistor T.

B

[2]

.................................................................. (ii) the power dissipation in T. .................................................................. .................................................................. [2]

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28 (Question B4 continued) Part 2 Electricity


Static electricity (a) A positively charged particle hangs from a vertical insulating string. The particle is brought above an electrically neutral metallic sphere that rests on an insulating support.

insulating string

positively charged particle

metallic sphere

insulating support

By considering the distribution of charge on the sphere, state and explain whether the tension in the string holding the charged particle will be less than, equal to or greater than the weight of the particle. (Assume that the mass of the string is negligible.) [3] ....................................................................... ....................................................................... ....................................................................... .......................................................................


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29 (Question B4, part 2 continued) (b)


Diagrams A, B and C show a sequence of events in which: A: the sphere in (a) is earthed (grounded), B: the earth is then removed while the charged particle remains in place, C: finally the charged particle is taken away.

A (i) (ii) from the sphere.

B

C

On each of the diagrams A, B and C draw the distribution of charge on the sphere. [3] Explain why work has to be done on the charged particle to move it away [2] .................................................................. ..................................................................


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30 (Question B4, part 2 continued) Current electricity (c) Define electromotive force (e.m.f.).


[1]

....................................................................... ....................................................................... (d) In the circuit below the battery has an e.m.f. of 12 V and an internal resistance of 5.0 . e.m.f. 12 V

60

X

30

30

Y

60

Calculate the (i) total resistance of the circuit. .................................................................. .................................................................. .................................................................. .................................................................. (ii) current in the internal resistance. .................................................................. .................................................................. [1] [3]


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31 (Question B4, part 2 continued) (iii) total power dissipated in the circuit.


[2]

.................................................................. .................................................................. (iv) potential difference between points X and Y. .................................................................. .................................................................. .................................................................. (e) A real (i.e. non-ideal) voltmeter is connected across points X and Y in the circuit in (d). Explain why the reading of this voltmeter will not be the same as your answer to (d) [2] (iv). ....................................................................... ....................................................................... [3]

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Electricity and Fields Questions