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PRE-LECTURE #31: Oscillating RLC Circuits (or Alternating Current Circuits)
Procedure: Open AC & DC circuit lab and click RUN NOW.
http://phet.colorado.edu/en/simulation/circuit-construction-kit-ac-virtual-lab
Once the simulation opens, drag an AC power supply, resistor, inductor, and capacitor onto the screen
and arrange the R, L, and C vertically on the right side. Connect them in series to each other. The
screen will be crowded so careful placement is important! Click on “current chart” and place it at upper
left corner of the screen – connect probe anywhere to measure the current in this series circuit. Then
click on “voltage chart” three times, move each to the left side under the current chart, and connect
each to measure vR(t), vL(t), and vC(t). Keep red probes toward top of screen, black toward the bottom.
Use + / - buttons on the chart to get full screen wave forms. (If current is not in phase with vR(t) move
current probe to opposite side of the power supply.)
A. Right click on each circuit component to set (or enter) the following values: f = 0.13 Hz, V = 10 Volt,
R = 10 , L = 12 H, and C = 0.13 F and compare the phase of each of the three voltage sine waves shown
on the four charts with respect to the current sine wave. On the reverse side of your paper, sketch on
one LARGE (appox. 8 in. x 10 in.) single set of axes: i(t), vR(t), vL(t), and vC(t) as a function of time. The
relative phases of each sine wave are important here. (See Figs. 31.7(b), 31.8(b), and 31.9(b) in your
textbook for guidance.) Note that two of the three voltage drops in this circuit are 180o out of phase
with each other and will cancel at the resonance frequency. Which two voltages are 180o out of phase?
Circle the two:
vR(t)
vL(t)
vC(t)
Should this cancellation result in an increase or decrease in the circuit current? INC___ or DEC___.
(Hint: Think about a DC circuit with a battery and three resistors in series. What happens to the
current if two resistors are removed and no longer provide voltage drops?)
B. Record below the values of your inductance and capacitance, calculate the value of the resonance
frequency in Hertz, and compare with the frequency set in your circuit: power supply freq = ____ Hz
fcalc = _____ Hz L = _____ Henry C = _____ Farads
f 
1
2
1
LC =
_____Hz
% diff = ____%
C. RESONANCE FREQUENCY
The resonance frequency is determined by the values
 of L and C as shown in the formula above. This
frequency results in vL(t) and vC(t) being exactly 1800 out of phase, thus canceling each other – these
voltage drops cancel each other and result in a larger current in the circuit! All other frequencies result
in different values for vL(t) and vC(t); thus they do not cancel and do not result in a larger current. This
larger current at the resonance frequency results in a larger voltage difference across the resistor (R).
This vR(t) voltage signal (and the information contained in it) is passed on to other circuits for further
amplification and signal processing (striping the audio frequencies from the transmitting, or resonance,
frequency). This is how your cell phone (which has a specific frequency assigned to it) can filter out
everyone else’s frequency. You don’t get their phone calls and they don’t get yours! See Fig. 31.19 in our
textbook to see a graph of this, and how the value of R determines the bandwidth (f) of the circuit. A
narrow bandwidth allows more signals (cell phone frequencies) to be assigned to, or squeezed into, a
certain region of the electromagnetic (EM) frequency spectrum. Our RLC circuit above can be coupled
to an antenna for EM wave transmission. In a receiving circuit our AC power supply is replaced by an
antenna which absorbs EM energy from a transmitted EM wave coming from a radio station transmitter.