Chapter 21
Electric Current and DirectCurrent Circuits
Units of Chapter 21
• Electric Current
• Resistance and Ohm’s Law
• Energy and Power in Electric Circuits
• Resistors in Series and Parallel
• Kirchhoff’s Rules
• Circuits Containing Capacitors
• RC Circuits
• Ammeters and Voltmeters
HW # 5
Pg. 754 – 759:
# 7, 8, 11, 19, 22, 28, 32, 44, 49, 73, 78
PHYS 1402.01
Due on Thursday, Oct. 10
PHYS 1402.02
Due on Thursday, Oct. 10
Practical resistors:
Example # 4
When a potential difference of 18 V is
applied to a given wire, it conducts 0.35 A
of current. What is the resistance of the
wire?
Resistance and Ohm’s Law
Two wires of the same length and diameter will
have different resistances if they are made of
different materials. This property of a material is
called the resistivity.
Resistance and Ohm’s Law
The difference between
insulators,
semiconductors, and
conductors can be clearly
seen in their resistivities:
Resistance and Ohm’s Law
In general, the resistance of materials goes up
as the temperature goes up, due to thermal
effects. This property can be used in
thermometers.
Resistivity decreases as the temperature
decreases, but there is a certain class of
materials called superconductors in which the
resistivity drops suddenly to zero at a finite
temperature, called the critical temperature TC.
Example # 5
Nichrome is a nickel –chromium alloy
used in heating applications like electric
toasters, because it has a relatively high
resistivity and heats up when current
passes through it. Suppose you have a
nichrome wire 0.20 mm in diameter and
75 cm long. ( a ) What’s its resistance?
( b) Find the current when a potential
difference of 120 V is connected across
the wire’s ends.
Energy and Power in Electric Circuits
When a charge moves across a potential
difference, its potential energy changes:
Therefore, the power it takes to do this is
Energy and Power in Electric Circuits
In materials for which Ohm’s law holds, the
power can also be written:
This power mostly becomes heat inside the
resistive material.
Example # 6 (Your turn)
Consider a 60 W light bulb, connected to
a 120 V voltage source.
What is the current passing
through the wire in the bulb?
(A) 0.5 A (B) 1.0 A (C) 2.0 A
(D) 240 A
What is the resistance of the
wire in the bulb?
(A) 0.5 W (B) 1.0 W (C) 2.0 W (D)
240 W
What is the current passing
through the wire in the bulb?
1. 0.5 A
2. 1.0 A
3. 2.0 A
4. 240 A
0%
0%
0%
0%
What is the resistant of the wire in
the bulb?
1. 0.5 A
2. 1.0 A
3. 2.0 A
4. 240 A
0%
0%
0%
0%
Conceptual Checkpoint 21 - 2
A battery that produces a potential difference V is
connected to a 5-W lightbulb. Later the 5-W
lightbult is replaced with a 10- W lightbulb. (a) In
which case does the battery supply more current?
1. 5 -W
2. 10-W
0%
0%
Conceptual Checkpoint 21 - 2
A battery that produces a potential difference V is
connected to a 5-W lightbulb. Later the 5-W
lightbult is replaced with a 10- W lightbulb. (b)
Which lightbulb has the greater resistance?
1. 5 -W
2. 10-W
0%
0%
Example # 7
pb. # 29 a) Find the power dissipated in a
25-Ω electric heater connected to a 120- V
outlet.
1. 0.60 kW
2. 1.0 kW
3. 0.58 kW
4. 2.6 kW
0%
0%
0%
0%
Energy Use:
Energy and Power in
Electric Circuits
When the electric company sends you a bill,
your usage is quoted in kilowatt-hours (kWh).
They are charging you for energy use, and kWh
are a measure of energy.
Example # 8
Electric utilities measure energy in kilowatt-hours (kWh),
where 1 kWh is the energy consumed if you use energy
at the rate of 1 kW for 1 hour. If your monthly electric bill
(30 days) is $100 and you pay 12.5c/kWh, what’s your
home’s average power consumption and average current,
assuming a 240-V potential difference between the wires
supplying your home?
1. 2.1 kW
2. 1.0 kW
3. 1.1 kW
4. 2.6 kW
0%
0%
0%
0%
Example # 8
Electric utilities measure energy in kilowatt-hours (kWh),
where 1 kWh is the energy consumed if you use energy
at the rate of 1 kW for 1 hour. If your monthly electric bill
(30 days) is $100 and you pay 12.5c/kWh, what’s your
home’s average power consumption and average current,
assuming a 240-V potential difference between the wires
supplying your home? Response for 2nd question
1. 4.0 A
2. 4.6 A
3. 3.0 A
4. 2.6 A
0%
0%
0%
0%
Example # 9
Several male students in the same dorm room want to
dry their hair. Having taken PHYS 1402 at UTPA, they
have set their hair dryers to the “low, “ 1000-W settings.
Assuming a standard 120-V how many hair dryers can
they operate simultaneously without tripping the 20-A
circuit breaker?
1. 9.0 A
2. 8.6 A
3. 9.03 A
4. 8.33 A
0%
0%
0%
0%
Resistors in Series
Resistors connected end to end are said to be in
series. They can be replaced by a single
equivalent resistance without changing the
current in the circuit.
Resistors in Series
Since the current through the series resistors
must be the same in each, and the total potential
difference is the sum of the potential differences
across each resistor, we find that the equivalent
resistance is:
Resistors in Series
The same current ( I ) must flow through each of
the resistors:
Ieq = I1 = I2 = I3
Total potential difference from point A to point B
must be the emf of the battery ε
Veq = ε = V1 + V2 + V3 …….
ε = I Req
Resistors in Series
Example # 10
Two resistors, one having half the resistance of the
other, are connected to a battery as shown on the white
board. What is the voltage across the bigger resistor?
1. A Vb / 2
2. B
Vb / 3
3. C
3Vb / 2
4. D
2Vb / 3
0%
0%
0%
0%
Example # 11
Two resistors, one having half the resistance of the
other, are connected to an emf battery as shown on the
board. What is the emf of the battery?
1. A IR / 2
2. B IR / 3
3. C
3IR / 2
4. D
2IR / 3
0%
0%
0%
0%
Resistors Parallel
Resistors are in parallel
when they are across the
same potential
difference; they can
again be replaced by a
single equivalent
resistance:
Resistors in Parallel
Using the fact that the potential difference
across each resistor is the same, and the total
current is the sum of the currents in each
resistor, we find:
Note that this equation gives you the inverse of
the resistance, not the resistance itself!
Resistors in Parallel
The potential difference across each resistor
will be the same.
Veq = ε = V1 = V2 = V3
The equivalent current will be the sum of all the
currents.
Ieq = I1 + I2 + I3
Example # 12
Two resistors are connected ( a ) in parallel, and ( b ) in
series, to a 24.0 V battery. See the diagraph on the white
board. What is the current through each resistor and
what is the equivalent resistance of each circuit?
Resistors Parallel
If a circuit is more complex, start with
combinations of resistors that are either purely
in series or in parallel. Replace these with their
equivalent resistances; as you go on you will be
able to replace more and more of them.
Kirchhoff’s Rules
More complex circuits cannot be broken down
into series and parallel pieces.
For these circuits, Kirchhoff’s rules are useful.
The junction rule is a consequence of charge
conservation; the loop rule is a consequence
of energy conservation.
Kirchhoff’s Rules
The junction rule: At any junction, the current
entering the junction must equal the current
leaving it.
Kirchhoff’s Rules
The loop rule: The algebraic sum of the potential
differences around a closed loop must be zero (it
must return to its original value at the original
point).
Kirchhoff’s Rules
Using Kirchhoff’s rules:
• The variables for which you are solving are the
currents through the resistors.
• You need as many independent equations as
you have variables to solve for.
• You will need both loop and junction rules.
Circuits Containing Capacitors
Capacitors can also be connected in series or in
parallel.
When capacitors are
connected in parallel,
the potential difference
across each one is the
same.
21-6 Circuits Containing Capacitors
Therefore, the equivalent capacitance is the
sum of the individual capacitances:
21-6 Circuits Containing Capacitors
Capacitors connected in
series do not have the
same potential difference
across them, but they do
all carry the same charge.
The total potential
difference is the sum of the
potential differences
across each one.
21-6 Circuits Containing Capacitors
Therefore, the equivalent capacitance is
Note that this equation gives you the inverse of
the capacitance, not the capacitance itself!
Capacitors in series combine like resistors in
parallel, and vice versa.
21-7 RC Circuits
In a circuit containing
only batteries and
capacitors, charge
appears almost
instantaneously on the
capacitors when the
circuit is connected.
However, if the circuit
contains resistors as
well, this is not the case.
21-7 RC Circuits
Using calculus, it can be shown that the charge
on the capacitor increases as:
Here, τ is the time constant of the circuit:
And
is the final charge on the capacitor, Q.
21-7 RC Circuits
Here is the charge vs. time for an RC circuit:
21-7 RC Circuits
It can be shown that the current in the circuit
has a related behavior:
21-8 Ammeters and Voltmeters
An ammeter is a device for measuring current,
and a voltmeter measures voltages.
The current in the circuit must flow through the
ammeter; therefore the ammeter should have
as low a resistance as possible, for the least
disturbance.
21-8 Ammeters and Voltmeters
A voltmeter measures the potential
drop between two points in a circuit.
It therefore is connected in parallel;
in order to minimize the effect on
the circuit, it should have as large a
resistance as possible.
Summary of Chapter 21
• Electric current is the flow of electric charge.
• Unit: ampere
• 1 A = 1 C/s
• A battery uses chemical reactions to maintain a
potential difference between its terminals.
• The potential difference between battery
terminals in ideal conditions is the emf.
• Work done by battery moving charge around
circuit:
Summary of Chapter 21
• Direction of current is the direction positive
charges would move.
• Ohm’s law:
• Relation of resistance to resistivity:
• Resistivity generally increases with
temperature.
• The resistance of a superconductor drops
suddenly to zero at the critical temperature, TC.
Summary of Chapter 21
• Power in an electric circuit:
• If the material obeys Ohm’s law,
• Energy equivalent of one kilowatt-hour:
• Equivalent resistance for resistors in series:
Summary of Chapter 21
• Inverse of the equivalent resistance of
resistors in series:
• Junction rule: All current that enters a
junction must also leave it.
• Loop rule: The algebraic sum of all potential
charges around a closed loop must be zero.
Summary of Chapter 21
• Equivalent capacitance of capacitors connected
in parallel:
• Inverse of the equivalent capacitance of
capacitors connected in series:
Summary of Chapter 21
• Charging a capacitor:
• Discharging a capacitor:
Summary of Chapter 21
• Ammeter: measures current. Is connected in
series. Resistance should be as small as
possible.
• Voltmeter: measures voltage. Is connected in
parallel. Resistance should be as large as
possible.