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Chapter 17

Electric Current and

Resistance

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Units of Chapter 17

Batteries and Direct Current

Current and Drift Velocity

Resistance and Ohm’s Law

Electric Power

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17.1 Batteries and Direct Current

Electric current is the

flow of electric

charge. A battery is a

source of electric

energy—it converts

chemical energy into

electric energy.

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17.1 Batteries and Direct Current

In a complete circuit, electrons flow from the

negative electrode to the positive one.

The positive electrode is called the anode; the

negative electrode is the cathode.

A battery provides a constant source of

voltage—it maintains a constant potential

difference between its terminals.

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Question 17.1 Connect the Battery

Which is the correct way to

light the lightbulb with the

battery?

d) all are correct

e) none are correct

a) c)b)

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Current can flow only if there is a continuous connection from

the negative terminal through the bulb to the positive terminal.

This is the case for only Fig. (3).

Question 17.1 Connect the Battery

Which is the correct way to

light the lightbulb with the

battery?

d) all are correct

e) none are correct

a) c)b)

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17.1 Batteries and Direct Current

The potential difference

between the battery

terminals when the battery

is not connected to

anything is called the

electromotive force, emf.

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17.1 Batteries and Direct CurrentThe actual terminal voltage of the battery is

always less than the emf, due to internal

resistance. Usually the difference is very

small.

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17.1 Batteries and Direct Current

When batteries are

connected in

series, the total

voltage is the sum

of the individual

voltages.

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17.1 Batteries and Direct Current

When batteries of

equal voltage are

connected in parallel,

the total voltage does

not change; each

battery supplies part

of the total current.

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17.1 Batteries and Direct Current

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17.2 Current and Drift Velocity

Current is the time rate of flow of charge.

SI unit of current: the ampere, A

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17.2 Current and Drift Velocity

Historically, the direction of current has been

taken to be from positive to negative; this is

opposite to the way electrons flow. However,

this seldom matters.

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How long would it take for a net charge

of 2.7 C to pass a location in a wire if it

is to carry a steady current of 4.0 mA?

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17.2 Current and Drift Velocity

Electrons do not flow like water in a pipe. In

the absence of voltage, they move randomly

at high speeds, due to their temperature.

When a voltage is

applied, a very small

drift velocity is added

to the thermal

motion, typically

around 1 mm/s; this

is enough to yield the

observed current.

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17.3 Resistance and Ohm’s Law

If there is a potential difference across a

conductor, how much current flows?

The ratio between the voltage and the

current is called the resistance.

SI unit of resistance: the ohm, Ω

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17.3 Resistance and Ohm’s Law

An ohmic material is one whose resistance

is constant.

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17.3 Resistance and Ohm’s Law

Ohm’s law is valid only for ohmic materials:

The resistance of a

particular object

depends on its

length, cross-

sectional area,

material, and

temperature.

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17.3 Resistance and Ohm’s Law

As expected, the resistance is proportional

to the length and inversely proportional to

the cross-sectional area:

The constant ρ is called the resistivity,

and is characteristic of the material.

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a) Ohm’s law is obeyed since the

current still increases when V

increases

b) Ohm’s law is not obeyed

c) this has nothing to do with Ohm’s

law

Question 17.2 Ohm’s Law

You double the voltage

across a certain conductor

and you observe the current

increases three times. What

can you conclude?

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a) Ohm’s law is obeyed since the

current still increases when V

increases

b) Ohm’s law is not obeyed

c) this has nothing to do with Ohm’s

law

Ohm’s law, V = IR, states that the

relationship between voltage and

current is linear. Thus, for a conductor

that obeys Ohm’s law, the current must

double when you double the voltage.

Question 17.2 Ohm’s Law

You double the voltage

across a certain conductor

and you observe the current

increases three times. What

can you conclude?

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Question 17.3a Wires I

Two wires, A and B, are made of the

same metal and have equal length,

but the resistance of wire A is four

times the resistance of wire B. How

do their diameters compare?

a) dA = 4dB

b) dA = 2dB

c) dA = dB

d) dA = 1/2dB

e) dA = 1/4dB

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The resistance of wire A is greater because its area is less than

wire B. Since area is related to radius (or diameter) squared, the

diameter of A must be two times less than the diameter of B.

Question 17.3a Wires I

R ρA

,

Two wires, A and B, are made of the

same metal and have equal length,

but the resistance of wire A is four

times the resistance of wire B. How

do their diameters compare?

a) dA = 4dB

b) dA = 2dB

c) dA = dB

d) dA = 1/2dB

e) dA = 1/4dB

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Question 17.3b Wires II

A wire of resistance R is

stretched uniformly (keeping its

volume constant) until it is twice

its original length. What happens

to the resistance?

a) it decreases by a factor of 4

b) it decreases by a factor of 2

c) it stays the same

d) it increases by a factor of 2

e) it increases by a factor of 4

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Keeping the volume (= area x length) constant means

that if the length is doubled, the area is halved.

Since , this increases the resistance by a

factor of 4.

Question 17.3b Wires II

RA

,

A wire of resistance R is

stretched uniformly (keeping its

volume constant) until it is twice

its original length. What happens

to the resistance?

a) it decreases by a factor of 4

b) it decreases by a factor of 2

c) it stays the same

d) it increases by a factor of 2

e) it increases by a factor of 4

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17.3 Resistance and Ohm’s LawIn this table, you can easily see the

differences between the resistivities of

conductors, semiconductors, and insulators.

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17.3 Resistance and Ohm’s Law

For many materials, the temperature

dependence of the resistivity is approximately

linear, as long as the temperature change is

not too large.

The constant α is called the temperature

coefficient of resistivity. Some values of α

are listed in the table on the previous page.

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17.3 Resistance and Ohm’s Law

Some materials exhibit a curious

phenomenon: at a very low temperature called

the critical temperature, their resistivity drops

abruptly to zero.

These are called superconductors; they have

a number of unique properties. They are

impractical for everyday home use, however,

as they must be cooled to cryogenic

temperatures.

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17.4 Electric Power

Power, as usual, is the rate at which work is

done. For work done by electricity:

Rewriting,

For ohmic materials, we can write:

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17.4 Electric Power

So, where does this power go? It is changed

to heat in resistive materials.

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Question 17.4 Dimmer

When you rotate the knob of a

light dimmer, what is being

changed in the electric circuit?

a) the power

b) the current

c) the voltage

d) both a) and b)

e) both b) and c)

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The voltage is provided at 120 V from the

outside. The light dimmer increases the

resistance and therefore decreases the current

that flows through the lightbulb.

Question 17.4 Dimmer

When you rotate the knob of a

light dimmer, what is being

changed in the electric circuit?

a) the power

b) the current

c) the voltage

d) both a) and b)

e) both b) and c)

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17.4 Electric Power

Electric appliances

are rated in watts,

assuming standard

household voltage.

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Question 17.5a Lightbulbs

Two lightbulbs operate at 120 V, but

one has a power rating of 25 W while

the other has a power rating of 100 W.

Which one has the greater

resistance?

a) the 25 W bulb

b) the 100 W bulb

c) both have the same

d) this has nothing to do

with resistance

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Since P = V2 / R , the bulb with the lower

power rating has to have the higher

resistance.

Question 17.5a Lightbulbs

Two lightbulbs operate at 120 V, but

one has a power rating of 25 W while

the other has a power rating of 100 W.

Which one has the greater

resistance?

a) the 25 W bulb

b) the 100 W bulb

c) both have the same

d) this has nothing to do

with resistance

Follow-up: Which one carries the greater current?

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17.4 Electric Power

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17.4 Electric Power

The electric company

typically bills us for

kilowatt-hours (kWh),

a unit of energy.

We can reduce our

energy usage by buying

efficient appliances.

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Question 17.5b Space Heaters

Two space heaters in your living

room are operated at 120 V.

Heater 1 has twice the resistance

of heater 2. Which one will give

off more heat?

a) heater 1

b) heater 2

c) both equally

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Using P = V2 / R, the heater with the smaller resistance

will have the larger power output. Thus, heater 2 will

give off more heat.

Question 17.5b Space Heaters

Two space heaters in your living

room are operated at 120 V.

Heater 1 has twice the resistance

of heater 2. Which one will give

off more heat?

a) heater 1

b) heater 2

c) both equally

Follow-up: Which one carries the greater current?

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Review of Chapter 17

A battery produces emf; positive terminal is

the anode, negative is the cathode.

emf is measured in volts; it is the number of

joules the battery supplies per coulomb of

charge.

An electric current can exist only in a

complete circuit.

Resistance:

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Review of Chapter 17

Ohm’s law is obeyed if the resistance is

constant:

The resistance of an object depends on its

length, cross-sectional area, and

resistivity.

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Review of Chapter 17

Power is the rate at which work is done.

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To move 5.0 C of charge from one electrode to

the other, a 12-V battery must do how much

work?

60 W

5.0 C

12 J

60 J

12 V

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A car's starter motor draws 59 A from the

car's battery during startup.

If the startup time is 2.1 s, how many

electrons pass a given location in the circuit

during that time?

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How long does it take for a charge of

4.70 C to pass through the cross-

sectional area of a wire that is carrying

a current of 0.47 A?

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In a dental X-ray machine, the accelerated

electrons move to the east. The conventional

current in the machine is in what direction?

west

east

you can't tell from the data given

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Imagine that some protons are moving to the left

at the same time that some electrons are moving

to the right past the same location.

Part A: Will the net current be to the right, to the

left, zero, or none of the preceding?

A, to the right. B to the left. C. Zero. D. None of

the preceding

Part B. In 4.0 S, 6.9 C of electrons flow to the

right at the same time that 5.2 C of protons flow

to the left. What are the direction of the current

due to the protons?

to the left

to the right

Part C. What are the magnitude of the current

due to the protons?

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What is the emf of a battery with a 0.19 Ω

internal resistance if the battery delivers 1.5 A

to an externally connected 6.0 Ω resistor?

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If you double the voltage across a resistor while

at the same time cutting its resistance to one-

fourth its original value, what happens to the

current in the resistor?

it increases by 8 times

it increases by four times

it doubles

you can't tell from the data given

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A battery acquires and stores

A, energy.

B, charge & potential but not energy.

C, energy, charge, & potential.

D, potential.

E, charge.

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If you connect two identical storage batteries

together in series ("+" to "-"), and place them

in a circuit, the combination will provide

A, twice the voltage, and the same current

will flow through each.

B, zero volts.

C, the same voltage and the same current

will flow through each.

D, twice the voltage, and different currents

will flow through each.

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The resistivity of most common metals

A, remains constant over wide temperature

ranges.

B, increases as the temperature increases.

C, varies randomly as the temperature

increases.

D, decreases as the temperature increases.

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When charging a battery, the terminal voltage

is ________ the battery emf.

A, zero, as is

B, less than

C, more than

D, equal to

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During a research experiment on the

conduction of current in the human body, a

medical technician attaches one electrode to

the wrist and a second to the shoulder of a

patient.

If 120 mV is applied across the two

electrodes and the resulting current is 14.0

mA, what is the overall resistance of the

patient's arm?