Chapter 17
Current and Resistance
Electric Current


Whenever electric charges of like signs
move, an electric current is said to exist
The current is the rate at which the
charge flows through this surface


Look at the charges flowing perpendicularly
to a surface of area A
Q
I 
t
The SI unit of current is Ampere (A)

1 A = 1 C/s
Electric Current, cont

The direction of the current is the
direction positive charge would flow

This is known as conventional current
direction


In a common conductor, such as copper, the
current is due to the motion of the negatively
charged electrons
It is common to refer to a moving
charge as a mobile charge carrier

A charge carrier can be positive or negative
Properties of a Current
Definition of a Current
Conservation of Current
 Iin   Iout
Checking Understanding
Rank the bulbs in the following circuit according to their
brightness, from brightest to dimmest.
A.
B.
C.
D.
ABCD
ABCD
ADBC
BCAD
Answer
Rank the bulbs in the following circuit according to their
brightness, from brightest to dimmest.
A.
B.
C.
D.
ABCD
ABCD
ADBC
BCAD
Meters in a Circuit –
Ammeter

An ammeter is used to measure current

In line with the bulb, all the charge passing
through the bulb also must pass through
the meter
Meters in a Circuit –
Voltmeter

A voltmeter is used to measure voltage
(potential difference)

Connects to the two ends of the bulb
Resistance


In a conductor, the voltage applied
across the ends of the conductor is
proportional to the current through
the conductor
The constant of proportionality is
the resistance of the conductor
V
R
I
Resistance, cont

Units of resistance are ohms (Ω)


1Ω=1V/A
Resistance in a circuit arises due to
collisions between the electrons
carrying the current with the fixed
atoms inside the conductor
Georg Simon Ohm



1787 – 1854
Formulated the
concept of
resistance
Discovered the
proportionality
between current
and voltages
Ohm’s Law


Experiments show that for many
materials, including most metals, the
resistance remains constant over a wide
range of applied voltages or currents
This statement has become known as
Ohm’s Law


ΔV = I R
Ohm’s Law is an empirical relationship
that is valid only for certain materials

Materials that obey Ohm’s Law are said to
be ohmic
Ohm’s Law, cont




An ohmic device
The resistance is
constant over a wide
range of voltages
The relationship
between current and
voltage is linear
The slope is related
to the resistance
Ohm’s Law, final



Non-ohmic materials
are those whose
resistance changes
with voltage or
current
The current-voltage
relationship is
nonlinear
A diode is a common
example of a nonohmic device
Reading Quiz
1. The charge carriers in metals are
A.
B.
C.
D.
electrons.
positrons.
protons.
a mix of protons and electrons.
Answer
1. The charge carriers in metals are
A.
B.
C.
D.
electrons.
positrons.
protons.
a mix of protons and electrons.
Slide 22-7
Reading Quiz
2. A battery is connected to a resistor. Increasing the resistance
of the resistor will
A. increase the current in the circuit.
B. decrease the current in the circuit.
C. not affect the current in the circuit.
Answer
2. A battery is connected to a resistor. Increasing the resistance
of the resistor will
A. increase the current in the circuit.
B. decrease the current in the circuit.
C. not affect the current in the circuit.
Reading Quiz
3. A battery is connected to a resistor. As charge flows, the
chemical energy of the battery is dissipated as
A.
B.
C.
D.
current.
voltage.
charge.
thermal energy.
Answer
3. A battery is connected to a resistor. As charge flows, the
chemical energy of the battery is dissipated as
A.
B.
C.
D.
current.
voltage.
charge.
thermal energy.
Resistivity

The resistance of an ohmic conductor is
proportional to its length, L, and
inversely proportional to its crosssectional area, A
L
R
A


ρ is the constant of proportionality and is
called the resistivity of the material
See table 17.1
Resistivity
The resistance of a wire
depends on its dimensions
and the resistivity of its
material:
Slide 22-22
Temperature Variation of
Resistivity

For most metals, resistivity
increases with increasing
temperature


With a higher temperature, the
metal’s constituent atoms vibrate
with increasing amplitude
The electrons find it more difficult to
pass through the atoms
Temperature Variation of
Resistivity, cont

For most metals, resistivity increases
approximately linearly with temperature
over a limited temperature range
  o [1  (T  To )]


ρ is the resistivity at some temperature T
ρo is the resistivity at some reference
temperature To


To is usually taken to be 20° C
 is the temperature coefficient of resistivity
Temperature Variation of
Resistance

Since the resistance of a conductor
with uniform cross sectional area is
proportional to the resistivity, you
can find the effect of temperature
on resistance
R  Ro [1  (T  To )]
Superconductors

A class of materials
and compounds
whose resistances
fall to virtually zero
below a certain
temperature, TC


TC is called the critical
temperature
The graph is the
same as a normal
metal above TC, but
suddenly drops to
zero at TC
Superconductors, cont

The value of TC is sensitive to




Chemical composition
Pressure
Crystalline structure
Once a current is set up in a
superconductor, it persists without
any applied voltage

Since R = 0
Superconductor, final


Good conductors
do not necessarily
exhibit
superconductivity
One application is
superconducting
magnets
Electrical Energy and
Power

In a circuit, as a charge moves through
the battery, the electrical potential
energy of the system is increased by
ΔQΔV


The chemical potential energy of the battery
decreases by the same amount
As the charge moves through a resistor,
it loses this potential energy during
collisions with atoms in the resistor

The temperature of the resistor will increase
Energy Transfer in the
Circuit


Consider the
circuit shown
Imagine a
quantity of
positive charge,
Q, moving
around the circuit
from point A back
to point A
Energy Transfer in the
Circuit, cont

Point A is the reference point


It is grounded and its potential is
taken to be zero
As the charge moves through the
battery from A to B, the potential
energy of the system increases by
QV

The chemical energy of the battery
decreases by the same amount
Energy Transfer in the
Circuit, final



As the charge moves through the
resistor, from C to D, it loses energy in
collisions with the atoms of the resistor
The energy is transferred to internal
energy
When the charge returns to A, the net
result is that some chemical energy of
the battery has been delivered to the
resistor and caused its temperature to
rise
Electrical Energy and
Power, cont

The rate at which the energy is
lost is the power
Q

V  I V
t

From Ohm’s Law, alternate forms
of power are
V
 I R 
R
2
2
Electrical Energy and
Power, final

The SI unit of power is Watt (W)


I must be in Amperes, R in ohms and
V in Volts
The unit of energy used by electric
companies is the kilowatt-hour


This is defined in terms of the unit of
power and the amount of time it is
supplied
1 kWh = 3.60 x 106 J
Checking Understanding
The wires below carry currents as noted. Rate the currents IA, IB
and IC:
A. I A  I B  I C
B. I B  I A  I C
C. I C  I A  I B
D. I A  I C  I B
E. I C  I B  I A
Answer
The wires below carry currents as noted. Rate the currents IA, IB
and IC:
A. I A  I B  I C
B. I B  I A  I C
C. I C > I A > I B
D. I A  I C  I B
E. I C  I B  I A
Batteries
The potential difference
between the terminals of a
battery, often called the
terminal voltage, is the
battery’s emf.
Wchem
Vbat 
e
q
Simple Circuits
The current is determined by
the potential difference and
the resistance of the wire:
Vwire
I
R
Checking Understanding
A battery is connected to a wire, and makes a current in the wire.
Which of the following changes would increase the current?
(1) Increasing the length of the wire; (2) keeping the wire the
same length, but making it thicker; (3) using a battery with a
higher-rated voltage; (4) making the wire into a coil, but keeping
its dimensions the same; (5) increasing the temperature of the
wire.
A.
B.
C.
D.
E.
All of the above
1 and 5
1, 4, and 5
2 and 3
None of the above
Answer
A battery is connected to a wire, and makes a current in the wire.
Which of the following changes would increase the current?
(1) Increasing the length of the wire; (2) keeping the wire the
same length, but making it thicker; (3) using a battery with a
higher-rated voltage; (4) making the wire into a coil, but keeping
its dimensions the same; (5) increasing the temperature of the
wire.
A.
B.
C.
D.
E.
All of the above
1 and 5
1, 4, and 5
2 and 3
None of the above
Checking Understanding: Measuring Light
Intensity
A battery is connected to a photoresistor. When light shines on this
resistor, it increases the number of charge carriers that are free to
move in the resistor. Now, the room lights are turned off, so less
light falls on the photoresistor. How does this affect the current in
the circuit?
A. The current increases.
B. The current decreases.
C. The current is not affected.
Answer
A battery is connected to a photoresistor. When light shines on this
resistor, it increases the number of charge carriers that are free to
move in the resistor. Now, the room lights are turned off, so less
light falls on the photoresistor. How does this affect the current in
the circuit?
A. The current increases.
B. The current decreases.
C. The current is not affected.
Power in Circuits
Energy and Power in Resistors
Checking Understanding
A resistor is connected to a 3.0 V battery; the power dissipated in
the resistor is 1.0 W. The battery is traded for a 6.0 V battery. The
power dissipated by the resistor is now
A.
B.
C.
D.
1.0 W
2.0 W
3.0 W
4.0 W
Answer
A resistor is connected to a 3.0 V battery; the power dissipated in
the resistor is 1.0 W. The battery is traded for a 6.0 V battery. The
power dissipated by the resistor is now
A.
B.
C.
D.
1.0 W
2.0 W
3.0 W
4.0 W
Summary
Additional Questions
1. A set of lightbulbs have different rated voltage and power,
as in the table below. Which one has the highest
resistance?
Bulb
A
B
C
D
E
Rated voltage
10 V
8V
12 V
6V
3V
Rated power
1W
1W
2W
2W
3W
Answer
1. A set of lightbulbs have different rated voltage and power,
as in the table below. Which one has the highest
resistance?
Bulb
A
B
C
D
E
Rated voltage
10 V
8V
12 V
6V
3V
Rated power
1W
1W
2W
2W
3W
Additional Questions
2. A set of lightbulbs have different rated voltage and power,
as in the table below. Which one has lowest resistance?
Bulb
A
B
C
D
E
Rated voltage
10 V
8V
12 V
6V
3V
Rated power
1W
1W
2W
2W
3W
Answer
2. A set of lightbulbs have different rated voltage and power,
as in the table below. Which one has lowest resistance?
Bulb
A
B
C
D
E
Rated voltage
10 V
8V
12 V
6V
3V
Rated power
1W
1W
2W
2W
3W
Additional Questions
3. A battery makes a circuit with a lightbulb as shown. Two
compasses are near the wires before and after the bulb in the
circuit. Which compass experiences a larger deflection?
A. Compass 1 experiences a larger deflection.
B. Compass 2 experiences a larger deflection.
C. Both compasses experience the same deflection.
Answer
3. A battery makes a circuit with a lightbulb as shown. Two
compasses are near the wires before and after the bulb in the
circuit. Which compass experiences a larger deflection?
A. Compass 1 experiences a larger deflection.
B. Compass 2 experiences a larger deflection.
C. Both compasses experience the same deflection.
Additional Questions
4. In Trial 1, a battery is connected to a single lightbulb and the
brightness noted. Now, in Trial 2, a second, identical, lightbulb
is added. How does the brightness of these two bulbs compare
to the brightness of the single bulb in Trial 1?
A. The brightness is greater.
B. The brightness is the same.
C. The brightness is less.
Answer
4. In Trial 1, a battery is connected to a single lightbulb and the
brightness noted. Now, in Trial 2, a second, identical, lightbulb
is added. How does the brightness of these two bulbs compare
to the brightness of the single bulb in Trial 1?
A. The brightness is greater.
B. The brightness is the same.
C. The brightness is less.
End of Chapter Problems
3, 12, 22, 28, 32, 35, 38, 39