PASCO EM-8656 AC_DC ELECTRONICS LABORATORY - Manual (Page 53)

49
012-05892A AC/DC Electronics Laboratory
®
Experiment 14: LRC Circuit
EQUIPMENT NEEDED:
– Computer and Science Workshop™ Interface
– Power Amplifier (CI-6552A)
– Voltage Sensor (CI-6503)
– AC/DC Electronics Lab Board (EM-8656): inductor coil & core, 10
Ω
resistor,
100
µ
F capacitor, wire lead
– LCR (inductance-capacitance-resistance) meter (SB-9754)
– (2) banana plug patch cords (such as SE-9750)
– graph paper
Purpose
The purpose of this experiment is to study resonance in an inductor-resistor-capacitor circuit
(LRC circuit) by examining the current through the circuit as a function of the frequency of the
applied voltage.
Theory
The amplitude of the AC current (I
o
) in a series LRC circuit is dependent on the amplitude of the
applied voltage (V
o
) and the impedance (Z).
I
o
=
V
o
Z
Since the impedance depends on frequency, the current varies with frequency:
Z
=
X
L
−
X
C
( )
2 +
R 2
where X
L
= inductive reactance =
ω
L, X
C
= capacitive reactance =
1
ω
C
, R = resistance, and
ω
=
angular frequency = 2
πν
(
ν
= linear frequency). The current will be maximum when the circuit
is driven at its resonant frequency:
ω
res
=
1
LC
One can show that, at resonance, X
L
= X
C
at resonance and thus the impedance (Z) is equal to R.
So at resonance the impedance is the lowest value possible and the current will be the largest
possible.
In this experiment the amplitude of the current vs. frequency is plotted. Since the current is a
maximum at the resonant frequency and is less for higher or lower frequencies, the graph is
expected to peak at the resonant frequency.