Chapter 25 Electric Currents and Resistance25-5 Electric Power Example 25-9: Electric heater. An electric heater draws a steady 15.0 A on a 120 V line. How much power does it require

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Lecture PowerPoints

Physics for Scientists and Engineers, with Modern

Physics, 4th edition

Giancoli

Chapter 25


Chapter 25Electric Currents and

Resistance

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• The Electric Battery

• Electric Current

• Ohm’s Law: Resistance and Resistors

• Resistivity

• Electric Power

Units of Chapter 25

• Power in Household Circuits

• Alternating Current


Volta discovered that electricity could be created if dissimilar metals were connected by a conductive solution called an electrolyte.

This is a simple electric cell.

25-1 The Electric Battery

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A battery transforms chemical energy into electrical energy.

Chemical reactions within the cell create a potential difference between the terminals by slowly dissolving them. This potential difference can be maintained even if a current is kept flowing, until one or the other terminal is completely dissolved.



Several cells connected together make a battery, although now we refer to a single cell as a battery as well.


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Electric current is the rate of flow of charge through a conductor:

Unit of electric current: the ampere, A:

1 A = 1 C/s.

25-2 Electric Current

The instantaneous current is given by:


A complete circuit is one where current can flow all the way around. Note that the schematic drawing doesn’t look much like the physical circuit!


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Example 25-1: Current is flow of charge.

A steady current of 2.5 A exists in a wire for 4.0 min. (a) How much total charge passed by a given point in the circuit during those 4.0 min? (b) How many electrons would this be?

electrons 108.3106.1

600 (b)

C 60060)(4.02.5 (a)

2119

e

Q nne Q

It Q t

QI


25-2 Electric CurrentConceptual Example 25-2: How to connect a battery.

What is wrong with each of the schemes shown for lighting a flashlight bulb with a flashlight battery and a single wire?

No Circuit – must include both battery terminals

OK

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By convention, current is defined as flowing from + to -. Electrons actually flow in the opposite direction, but not all currents consist of electrons.



Experimentally, it is found that the current in a wire is proportional to the potential difference between its ends:

25-3 Ohm’s Law: Resistance and Resistors

VI

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The ratio of voltage to current is called the resistance:



In many conductors, the resistance is independent of the voltage; this relationship is called Ohm’s law. Materials that do not follow Ohm’s law are called nonohmic.

Unit of resistance: the ohm, Ω:

1 Ω = 1 V/A.


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Conceptual Example 25-3: Current and potential.

Current I enters a resistor R as shown. (a) Is the potential higher at point A or at point B? (b) Is the current greater at point A or at point B?

(a) Higher at point A – current flows from high to low potential

(b) The same – all charge flowing past A also flows past B



Example 25-4: Flashlight bulb resistance.

A small flashlight bulb draws 300 mA from its 1.5 V battery. (a) What is the resistance of the bulb? (b) If the battery becomes weak and the voltage drops to 1.2 V, how would the current change?

mA 240A 0.240.5

2.1 (b)

0.510300

5.1 )(

3

R

VI

I

VRa

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Standard resistors are manufactured for use in electric circuits; they are color-coded to indicate their value and precision.




This is the standard resistor color code. Note that the colors from red to violet are in the order they appear in a rainbow.

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Resistor Colour Code:

Black 0

Eg: Red, Violet, YellowRed = 2Violet = 7Yellow = 4 (zeroes) R = 270000 = 270 kBrown 1

Red 2

Orange 3

Yellow 4

Green 5

Blue 6

Violet 7

Grey 8

White 9


Some clarifications:

• Batteries maintain a (nearly) constant potential difference; the current varies.

• Resistance is a property of a material or device.

• Current is not a vector but it does have a direction.

• Current and charge do not get used up. Whatever charge goes in one end of a circuit comes out the other end.


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The resistance of a wire is directly proportional to its length and inversely proportional to its cross-sectional area:

The constant ρ, the resistivity, is characteristic of the material.

25-4 Resistivity

AR

l


25-4 ResistivityThis table gives the resistivity and temperature coefficients of typical conductors, semiconductors, and insulators.

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25-4 ResistivityExample 25-5: Speaker wires.

Suppose you want to connect your stereo to remote speakers.

(a) If each wire must be 20 m long, what diameter copper wire should you use to keep the resistance less than 0.10 Ω per wire?

(b) If the current to each speaker is 4.0 A, what is the potential difference, or voltage drop, across each wire?


25-4 ResistivityExample 25-5: Speaker wires.

(a) l = 20 m, R = 0.10 Ω per wire( = 1.68x10-8 .m)

mm 2.1m 0.0021

1.0

201068.14

44

8

2

πR

ρD

Dπ

ρ

A

ρR

lll

(b) I = 4.0 A, V = ?

V 0.400.14.0 IRV

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25-4 Resistivity

Conceptual Example 25-6: Stretching changes resistance.

Suppose a wire of resistance R could be stretched uniformly until it was twice its original length. What would happen to its resistance?

The total volume of the wire should stay the same; therefore if the length doubles, the cross-sectional area is halved. This increases the resistance by a factor of 4. (R = l/A)


For any given material, the resistivity increases with temperature:

Semiconductors are complex materials, and may have resistivities that decrease with temperature.

25-4 Resistivity

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25-4 Resistivity

Example 25-7: Resistance thermometer.

The variation in electrical resistance with temperature can be used to make precise temperature measurements. Platinum is commonly used since it is relatively free from corrosive effects and has a high melting point. Suppose at 20.0°C the resistance of a platinum resistance thermometer is 164.2 Ω. When placed in a particular solution, the resistance is 187.4 Ω. What is the temperature of this solution?


Example 25-7: Resistance thermometer.

From Table 25.1: Platinum: 20C = 0 = 10.60x10-8 .m

= 0.003927 /CR20C = R0 = 164.2 , RT = 187.4 , T = 20C

C 56.011

11

constant and for Since

1

00

T

000

T

0

T

00T

TR

RT

TTTTR

R

ARA

R

TT

ll

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Power, as in kinematics, is the energy transformed by a device per unit time:

25-5 Electric Power

or

Vdt

dq

dt

dUP

VdqdUqV U

Power

Since

IVP


The unit of power is the watt, W.

For ohmic devices, we can make the substitutions:

25-5 Electric Power

R

VV

R

VIVP

RIIRIIVP2

2)(

R

VRIVIP

22

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25-5 Electric Power

Example 25-8: Headlights.

Calculate the resistance of a 40 W automobile headlight designed for 12 V.

6.340

12222

P

VR

R

VP


What you pay for on your electric bill is not power, but energy – the power consumption multiplied by the time.

We have been measuring energy in joules, but the electric company measures it in kilowatt-hours, kWh:

1 kWh = (1000 W)(3600 s) = 3.60 x 106 J.

25-5 Electric Power

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25-5 Electric Power

Example 25-9: Electric heater.

An electric heater draws a steady 15.0 A on a 120 V line. How much power does it require and how much does it cost per month (30 days) if it operates 3.0 h per day and the electric company charges 9.2 cents per kWh?

$14.90 c 1490 1629.2 costs c/kWh this 9.2At

kWh 16230)(3.01.8 kWh

kW 1.8 W18000.15120 :Power

VIP


Example 25-10: Lightning bolt.

Lightning is a spectacular example of electric current in a natural phenomenon. There is much variability to lightning bolts, but a typical event can transfer 109 J of energy across a potential difference of perhaps 5 x 107 V during a time interval of about 0.2 s. Use this information to estimate (a) the total amount of charge transferred between cloud and ground, (b) the current in the lightning bolt, and (c) the average power delivered over the 0.2 s.

GW 5 W1052.0

10Power (c)

A 1002.0

20 (b)

C 20105

10Energy (a)

99

7

9

t

UP

t

QI

V

UQVQU

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The wires used in homes to carry electricity have very low resistance. However, if the current is high enough, the power will increase and the wires can become hot enough to start a fire.

To avoid this, we use fuses or circuit breakers, which disconnect when the current goes above a predetermined value.

25-6 Power in Household Circuits


Fuses are one-use items – if they blow, the fuse is destroyed and must be replaced.


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Circuit breakers, which are now much more common in homes than they once were, are switches that will open if the current is too high; they can then be reset.



One type of circuit breaker. (b) The electric current passes through a bimetallic strip. When the current exceeds a safe level, the heating of the bimetallic strip causes the strip to bend so far to the left that the notch in the spring-loaded metal strip drops down over the end of the bimetallic strip; (c) the circuit then opens at the contact points (one is attached to the metal strip) and the outside switch is also flipped. As soon as the bimetallic strip cools down, it can be reset using the outside switch.


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25-6 Power in Household CircuitsExample 25-11: Will a fuse blow? Assume 20 A fuse or circuit breaker.

Determine the total current drawn by all the devices in the circuit shown.

A 28.7

A 0.01120

1200

A 9.2120

350

A 0.51120

1800

A 0.83120

100

Total

DryerHair

Stereo

Heater

Light

I

I

I

I

I

V

PIVIP

Fuse would blow – Heater should be on a separate circuit.



Conceptual Example 25-12: A dangerous extension cord.

Your 1800 W portable electric heater is too far from your desk to warm your feet. Its cord is too short, so you plug it into an extension cord rated at 11 A. Why is this dangerous?

An 1800-W heater operating at 120 V draws 15 A of current, which exceeds the rating of the extension cord. This creates a risk of overheating and fire.

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Current from a battery flows steadily in one direction (direct current, DC). Current from a power plant varies sinusoidally (alternating current, AC).

25-7 Alternating Current


The voltage varies sinusoidally with time:

as does the current:


f = frequency = 2 f

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Multiplying the current and the voltage gives the power:



Usually we are interested in the average power:


.

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The current and voltage both have average values of zero, so we square them, take the average, then take the square root, yielding the root-mean-square (rms) value. The rms value is the effective value of the current or voltage, i.e, the steady DC value that would result in the same energy dissipation.




Example 25-13: Hair dryer.

(a) Calculate the resistance and the peak current in a 1000 W hair dryer connected to a 120 V line. (b) What happens if it is connected to a 240 V line in Britain?

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Example 25-13: Hair dryer.

(a) Calculate the resistance and the peak current in a 1000 W hair dryer connected to a 120 V line.

(b) What happens if it is connected to a 240 V line in Britain?

A 11.84.14

100022

2

Ω 14.41000

120

Peak

Peakrms

2rms

22rms

2rms

R

PI

I

R

PIRIP

P

VR

R

VP

dryer)hair for good(not 4 offactor aby

power increase would doublingR rms

2rms V

VP


• A battery is a source of constant potential difference.

• Electric current is the rate of flow of electric charge.

• Conventional current is in the direction that positive charge would flow.

• Resistance is the ratio of voltage to current:

Summary of Chapter 25

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• Ohmic materials have constant resistance, independent of voltage.

• Resistance is determined by shape and material:

• ρ is the resistivity.



• Power in an electric circuit:

• Direct current is constant.

• Alternating current varies sinusoidally:


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• The average (rms) current and voltage:


Documents

Chapter 25 Electric Currents and Resistance25-5 Electric Power Example 25-9: Electric heater. An electric heater draws a steady 15.0 A on a 120 V line. How much power does it require