Lab 10: Capacitors and inductors in
AC circuits, and electrical resonance
1
Introduction
Capacitors and inductors can be used to store energy
in electrical circuits in the form of electric fields and
magnetic fields respectively.
This lab will introduce
you to the behavior of these elements in alternating
current (AC) circuits. The lab will also cover exper
iments associated with the phenomenon of resonance
in simple circuits with a resistor, an inductor and a
capacitor.
Depending on the values of the inductor
and capacitor, these circuits can be made to select or
respond to specific resonant frequencies. Such circuits
are used in radios and television sets to tune to various
frequencies or channels. The principle of resonance is
widely used in the design of electrical circuits.
EXERCISES 1 AND 2 PERTAIN TO THE
BACKGROUND
CONCEPTS
AND
EXER
CISES 3  5 PERTAIN TO THE EXPERI
MENTAL SECTIONS.
2
Background
When a resistor is connected to an AC voltage source,
the voltage is given by,
V
(
t
) =
V
0
sin (
ωt
)
(1)
The current through the resistor is simply given by
Ohm’s law as,
I
(
t
) =
V
0
R
sin (
ωt
)
(2)
The current has the same frequency (
f
=
ω
2
π
) and
phase as the voltage source.
When the AC source is connected to a capacitor
C
,
the charge on the plates of the capacitor is given by,
Q
(
t
) =
CV
(
t
)
(3)
Differentiating equation 3, and using
I
=
dQ
dt
, we get,
I
=
C
dV
dt
(4)
MT65
MT86
MT67
MT86MT40MT116MT41
MT116
MT73MT40MT116MT41
MT116
MT84MT47MT50
MT84
MT84MT47MT50
MT84
Figure 1: Voltage and current in an AC capacitor circuit. The
time period
T
=
1
f
Since
V
=
V
0
sin (
ωt
), equation 4 gives,
I
=
ωCV
0
cos (
ωt
) =
ωCV
0
sin (
ωt
+
π
2
)
(5)
Equation 5 shows that the capacitor introduces a
phase difference between the voltage and current since
the current in the capacitor leads the voltage by
90
◦
(figure 1). The quantity
ωCV
0
in equation 5 can
be identified as the amplitude of the current
I
0
.
In
analogy with Ohm’s law we can write,
I
0
=
V
0
X
C
(6)
where the impedance
X
C
is the capacitive reactance
(measured in ohms),
X
C
=
1
ωC
.
The impedance is
clearly frequency dependent.
At high frequencies it
tends to zero since the current through the capacitor
(
C
dV
dt
) increases with frequency.
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 Spring '10
 Hor.
 Electrical Circuits, Energy, Alternating Current, Inductor

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