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Chapter 26
AC Electricity
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PowerPoint® Lectures for
College Physics: A Strategic Approach, Second Edition
26 AC Electricity
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Slide 26-2
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Slide 26-3
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Slide 26-5
An AC Voltage Source
The circuit symbol
for an AC voltage
source
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Slide 26-10
Resistor Circuits
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Resistor Voltages and Currents
Lowercase symbols represent
instantaneous values of current or
voltage. They change sinusoidally with
time.
Uppercase symbols represent
peak values of current or
voltage. They are fixed
quantities.
vR  VRcos(2πft )
VR VRcos(2πft )
iR 

 IRcos(2πft )
R
R
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Slide 26-12
AC Power in Resistors
1 2
R= 2 R
P
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I R
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Root-Mean-Square Current and Voltage
If we define
IR
Irms 
2
and
VR
Vrms 
2
then we can write
 IR 
2
PR  
 R  ( Irms) R
 2
2
and
The expressions for AC power are identical to those used for DC
currents if rms currents and voltages are used.
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Slide 26-14
Transformers
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Checking Understanding
If the primary coil of wire on a transformer is kept the same and
the number of turns of wire on the secondary is increased, how will
this affect the voltage observed at the secondary?
A. The voltage will increase.
B. The voltage will stay the same.
C. The voltage will decrease.
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Slide 26-16
Answer
If the primary coil of wire on a transformer is kept the same and
the number of turns of wire on the secondary is increased, how will
this affect the voltage observed at the secondary?
A. The voltage will increase.
B. The voltage will stay the same.
C. The voltage will decrease.
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Slide 26-17
Example Problem
A 120 V (rms) AC power supply is connected to a motor, which is
rated at 100 W.
A.
What is the rms current in the circuit?
Now suppose that the wires used to connect the motor to the
power supply have a resistance of 7.0 .
B.
Assume that the rms current stays the same. What is the
voltage drop across the resistance of the wires? What is
the voltage at the motor now?
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Slide 26-18
Example Problem
Clearly this is untenable. Now suppose the power supply is
1200 V, and the motor is rated at 100 W at this higher voltage.
C. What is the current in the circuit, assuming no resistance
in the wires?
D. If the wires have a resistance of 7.0 , what is the voltage
drop across the wires? The voltage at the motor?
Now suppose the power supply is increased to 12,000 V, and the
motor is rated at 100 W at this still higher voltage.
E.
F.
What is the current in the circuit, assuming no resistance
in the wires?
If the wires have a resistance of 7.0 , what is the voltage
drop across the wires? The voltage at the motor?
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Transmission of Electrical Power
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Slide 26-20
Two-Phase Power
to Your Home
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Example Problem
The following devices are plugged into outlets on the same 120 V
circuit in a house. This circuit is protected with a 15-A circuit
breaker.
Device
Power
Computer
250 W
Heater
900 W
Lamp
100 W
Stereo
120 W
Is there too much current in the circuit—that is, does the circuit
breaker blow?
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Slide 26-22
Physiological Effects and Electrical Safety
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Electrical Safety
V
V
480 V
I


 48 mA
Req Rboots 10 MV
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Slide 26-24
Example Problem
Suppose a person is standing, barefoot, on wet ground. The
resistance of the skin on each foot is 300 . He now grabs an
improperly wired device with his right hand—establishing a
connection to the hot wire of the electric supply. His hand is a
bit sweaty, so the resistance of the skin is only 1.2 .
A.
B.
What current will flow through his body?
Will this be large enough for him to feel? Large
enough to be dangerous?
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Slide 26-25
Capacitor Circuits
vC  VC cos(2πft )
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Voltage, Charge, and
Current for a Capacitor
in an AC Circuit
where
1
XC 
2πfC
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Capacitive Reactance
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Inductance and Inductors
i L
vL  L
t
Units of inductance:
1 henry
1 henry
 1 H 1 H
V s/A
nry  1 H
1 V1s/A
1  1s   s
V  s/A  1   s
The circuit symbol for
an inductor
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Inductor Circuits
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Inductor Currents and Voltages
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Inductive Reactance
VL  L(2πfIL)  (2πfL) IL
or
where
XL  2πfL
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Checking Understanding
An isolation transformer—basically a 1:1 transformer—is
connected into a circuit with identical light bulbs on both the
primary and secondary circuits. What will happen to the
brightness of the bulb on the primary if you remove the bulb on
the secondary?
A.
B.
C.
D.
E.
It will become much brighter.
It will become slightly brighter.
It will remain the same brightness.
It will become slightly dimmer.
It will become much dimmer.
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Slide 26-33
Answer
An isolation transformer— basically a 1:1 transformer— is
connected into a circuit with identical light bulbs on both the
primary and secondary circuits. What will happen to the
brightness of the bulb on the primary if you remove the bulb on
the secondary?
A.
B.
C.
D.
E.
It will become much brighter.
It will become slightly brighter.
It will remain the same brightness.
It will become slightly dimmer.
It will become much dimmer.
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LC Circuits
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Energy of an LC Circuit and a Block on a Spring
Block on spring:
1 k
f 
2π m
LC circuit:
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The RLC Circuit
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The Driven RLC Circuit
1
f0 
2π LC
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e0
Imax 
R
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The Driven RLC Circuit for Different Values of R
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Additional Question
Suppose that an ideal transformer has 400 turns in its primary
coil and 100 turns in its secondary coil. The primary coil is
connected to a 120-V (rms) electric outlet and carries an rms
current of 10 mA. What are the rms values of the voltage and
current for the secondary?
A.
B.
C.
D.
480 V, 40 mA
480 V, 2.5 mA
30 V, 40 mA
30 V, 2.5 mA
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Slide 26-40
Answer
Suppose that an ideal transformer has 400 turns in its primary
coil and 100 turns in its secondary coil. The primary coil is
connected to a 120-V (rms) electric outlet and carries an rms
current of 10 mA. What are the rms values of the voltage and
current for the secondary?
A.
B.
C.
D.
480 V, 40 mA
480 V, 2.5 mA
30 V, 40 mA
30 V, 2.5 mA
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Slide 26-41