# Lab 12 - The RLC Series Circuit by nuhman10

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Physics Laboratory
The RLC Series Circuit

In this experiment, we will record and graph how the current amplitude in an RLC series circuit responds
as the frequency of the inputted signal changes, and will use the graph to determine the experimental
resonant frequency of the circuit.. Through our analysis, we know that the current amplitude is a
maximum at the resonant frequency of the system. This experimental value will then be compared to the
theoretical value.

I.   Relationship between the Current Amplitude Im and frequency f in the RLC Series Circuit

A.   A circuit consisting of a resistor R, inductor L,
and capacitor C are connected in series and
R                         C
then connected to a function generator                                  L
producing a sinusoidal signal with a constant
voltage amplitude Vm . We know that the
relationship between the current amplitude
and the voltage amplitude is Vm = ImZ ,
where Z is the impedance of the RLC series                           v = Vm sin t
circuit. The current amplitude can then be
written as

Vm
Im                          .

R 2  L  1 C   
2

Rewrite this in terms of the frequency f.

Find the frequency at which the current amplitude is a maximum. The frequency is called the
resonant frequency of the circuit. Show and explain how you found this value.
B.    Draw the graph of how the current amplitude Im varies with frequency f. Be sure to show the
resonant frequency.
Im

f

II.   The Experimental Set-up

A.    Equipment:    oscilloscope w/ two BNC leads                inductor
function generator w/ one BNC lead           capacitance box
two wire connectors                          decade resistance box

B.    Connect a function generator, inductor, capacitance
box and decade resistance box as an RLC series circuit.
Be sure that the resistance box is connected to the
ground terminal of the AC generator. Connect Channel
Inductor        Channel 2
1 of the oscilloscope across the resistance box and
Channel 2 across the entire RLC circuit. Remember the
ground of the AC generator and the ground of the
oscilloscope must be connected to the same location.
the decade resistance box at 100 ohms (500 ohms) and          Generator                  Capacitance
Box
the value of capacitance to between 0.006 and 0.060 F.
Channel 1
C.    Instead of measuring the current amplitude directly,
we will measure the voltage amplitude across the                  Decade
Resistance
decade resistance box. In this case remember that the
Box
voltage amplitude across the resistor is proportional to
the current amplitude (VmR = ImR). We will also
divide this value by the voltage amplitude coming
from the function generator (Vm) in order to eliminate any effects caused by variations in the voltage
supplied by the function generator. This is referred to as “normalizing.”

D.    Data: Report your values of resistance, capacitance, and inductance. Adjust the frequency of your
function generator to 1000 Hz and record the subsequent voltages on channel 1 (V1 = VmR) and
channel 2 (V2 = Vm). Repeat these measurements at 2000, 4000, 7000, 10000, 20000, 40000, 70000, and
100000 Hz. Make more measurements close to and around the resonant frequency so that you can
draw a smooth curve through the points.
L = _______________ mH, RL = _______________ ohms; C = _______________ F

Trial 1 – R = 100 ohms                        Trial 2 – R = 500 ohms
Frequency
(Hz)      Ch-1 voltage   Ch-2 voltage                  Ch-1 voltage    Ch-2 voltage
V1/V2                                         V1/V2
V1 (volts)     V2 (volts)                    V1 (volts)      V2 (volts)
1000

2000

4000

7000

10000

20000

40000

70000

100000

E.   Graph these two sets of data on the same sheet of two cycle semilog graph paper, and draw a

F.   Calculations and Results: Locate the resonant frequency for each set of data on your graph and
report these values as your experimental values of the resonant frequency. Calculate your
theoretical value from the values of your circuit elements and report this value. Find the percentage
error between the experimental values and the theoretical value.
Experimental Value of          Theoretical Value of
Resonant Frequency            Resonant Frequency              Percentage Error
(Hz)                          (Hz)

Trisl 1

Trial 2

III. Questions

A.   Does changing the value of resistance in the circuit affect the value of the resonant frequency?
Explain.

B.   Which of the two circuits above when connected to an antenna would make a better receiver for a