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A30.2
A current i flows through an inductor L in
the direction from point b toward point a.
There is zero resistance in the wires of the
inductor. If the current is decreasing,
A. the potential is greater at point a than at point b.
B. the potential is less at point a than at point b.
C. The answer depends on the magnitude of di/dt compared
to the magnitude of i.
D. The answer depends on the value of the inductance L.
E. both C. and D. are correct.
© 2012 Pearson Education, Inc.
Chapter 31
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Alternating Current Circuits
Phasors and alternating currents

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The left diagram shows the voltage across an AC source as a
function of time
On the right is a simple phasor diagram.
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D’Arsonval galvanometer
•
•
A d’Arsonval galvanometer measures the current through
it (see Figures 26.13 and 26.14 below).
Many analog electrical instruments, such as ammeters
and voltmeters, use a galvanometer in their design.
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Root-mean-square values

To measure alternating current you
need something more complicated
than a simple analog voltmeter – e.g., a
circuit like the one to the right.
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Resistor in an ac circuit
•
•
Ohm’s Law gives the
voltage amplitude across a
resistor: VR = IR.
Figure 31.7 shows the
circuit, the current and
voltage as functions of time,
and a phasor.
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Inductor in an ac circuit
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•
The voltage amplitude across the inductor
is VL = IXL.
The voltage leads the current by 90◦
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Capacitance in an ac circuit
•
•
The voltage amplitude across the capacitor
is VC = IXC
The voltage follows the current by 90◦
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Comparing ac circuit elements
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•
Table 31.1 summarizes the characteristics of a resistor,
an inductor, and a capacitor in an ac circuit.
Figure 31.11 (below) shows graphs of resistance and
reactance.
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A useful application: the loudspeaker
•
The woofer (low tones) and
the tweeter (high tones) are
connected in parallel across
the amplifier output. (See
Figure 31.12 shown here.)
© 2012 Pearson Education, Inc.
Q31.1
A resistor is connected across an ac
source as shown. For this circuit, what
is the relationship between the
instantaneous current i through the
resistor and the instantaneous voltage
vab across the resistor?
A. i is maximum at the same time as vab.
B. i is maximum one-quarter cycle before vab.
C. i is maximum one-quarter cycle after vab.
D. not enough information given to decide
© 2012 Pearson Education, Inc.
A31.1
A resistor is connected across an ac
source as shown. For this circuit, what
is the relationship between the
instantaneous current i through the
resistor and the instantaneous voltage
vab across the resistor?
A. i is maximum at the same time as vab.
B. i is maximum one-quarter cycle before vab.
C. i is maximum one-quarter cycle after vab.
D. not enough information given to decide
© 2012 Pearson Education, Inc.
Q31.2
An inductor is connected across an ac
source as shown. For this circuit, what
is the relationship between the
instantaneous current i through the
inductor and the instantaneous voltage
vab across the inductor?
A. i is maximum at the same time as vab.
B. i is maximum one-quarter cycle before vab.
C. i is maximum one-quarter cycle after vab.
D. not enough information given to decide
© 2012 Pearson Education, Inc.
A31.2
An inductor is connected across an ac
source as shown. For this circuit, what
is the relationship between the
instantaneous current i through the
inductor and the instantaneous voltage
vab across the inductor?
A. i is maximum at the same time as vab.
B. i is maximum one-quarter cycle before vab.
C. i is maximum one-quarter cycle after vab.
D. not enough information given to decide
© 2012 Pearson Education, Inc.
Q31.3
A capacitor is connected across an ac
source as shown. For this circuit, what
is the relationship between the
instantaneous current i through the
capacitor and the instantaneous voltage
vab across the capacitor?
A. i is maximum at the same time as vab.
B. i is maximum one-quarter cycle before vab.
C. i is maximum one-quarter cycle after vab.
D. not enough information given to decide
© 2012 Pearson Education, Inc.
A31.3
A capacitor is connected across an ac
source as shown. For this circuit, what
is the relationship between the
instantaneous current i through the
capacitor and the instantaneous voltage
vab across the capacitor?
A. i is maximum at the same time as vab.
B. i is maximum one-quarter cycle before vab.
C. i is maximum one-quarter cycle after vab.
D. not enough information given to decide
© 2012 Pearson Education, Inc.