EXPERIMENT 5 Series Resonance in AC Circuits Figure 1

Physics 112 Laboratory Exp. 5 – Series Resonance in AC Circuits (2004 Fall)
Note, in Equations (1)-(4) the maximum values of the AC currents and voltages are used rather
than the effective values I and V. Since I = 0.707 i max and V = 0.707 v max , we are free to use either set
of values. Since it is easier to obtain i max and V max from the screen of the oscilloscope, we use the
maximum values here.
(X L - X C ) is the equivalent reactance between points a and b in Figure 1. This part of the circuit
consists of an inductor and a capacitor in series. The minus sign of X C indicates that the voltage across
the inductor is 180° out of phase with the voltage across the capacitor. The maximum voltage V L+C
between points a and b is given by:
V L+C = i max (X L -X C ) (6)
There is a specific frequency, called the resonant frequency, f res , at which X L = X C . The theoretical
value of f res is obtained by setting
leading to
X L = 2πf res L equal to X
f res
C
1
=
2π
f
res
C
1 1
= (7)
2π
LC
At resonance, according to Equation (5) and Figure 2, Z = R. Therefore, i max = V max /R and the
current in the circuit has its maximum value. Also, Equation (6) predicts that V L+C = 0 since X L - X C
= 0. In practice, V L+C is a minimum rather than zero at resonance because of the small amount of
resistance between points a and b due to the resistance of the inductance coil.
In this experiment, you will find f res for a particular RLC circuit by noting where V L+C is a
minimum. This experimental value of f res will then be compared to the theoretical value given by
Equation (7).
Apparatus:
Fixed-value inductor, capacitance box, resistance box, AC ammeter, oscilloscope, signal
generator.
v.2004-sep-10 (IMG)
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