Experiment 12: An AC Circuit
PART ONE: AC Voltages
In an AC circuit, we wish to see if calculated and observed voltages match, and if the phases of the
voltages are as predicted. A resistor, inductor and capacitor are connected in series across a
function generator. The amplitude of the voltage and the phase of the voltage across each of these is
observed using an oscilloscope.
CALCULATIONS: Unless you are informed otherwise, R = 500 Ω, L = 5.0 mH, C = .01 μF.
These are to be placed in series with a 2 volt, 15,000 Hz emf. Find the impedance of the circuit, the
current, and the potential difference across each of the three circuit elements: the capacitor, resistor
and inductor. (Solve this problem mathematically.)
EXPERIMENTAL PROCEDURE: Now, check your
results for VL, VC, and VR. Obtain the resistor, inductor,
and capacitor and set up this circuit. The three boxes are
the resistor, inductor, and capacitor. Which one is which is
not important. No black wire is needed on EXT TRIG.
Push the EXT TRIG button, located under TIMEBASE. The triggering circuits are what make the
spot drawing the trace start moving across the screen. When triggering externally, on the signal
from the function generator, the spot will wait until the function generator reaches a certain voltage.
The scope will then start drawing the wave from whatever point the signal being displayed has
reached at that moment. Signals with different phases will be at different points in their cycles, so
this lets you see the phase differences between R, L and C.
Adjust attenuation on the function generator to a 2.0 V output as measured by the scope. Normally,
V and I stand for RMS values. However, amplitude is easier to read from an oscilloscope and
behaves the same way. So, if you set the source for a 2.0 V amplitude, the amplitudes of VL, VC,
and VR should match what you calculated.
The frequency dials on some of the function generators are a little off. Check it: At 15,000 Hz, a
period should be 6 2/3 cm long at 10 s/cm. If not, ask the instructor if it's the function generator or
scope which is miscalibrated.
When the function generator has been set to 2 V, move the scope's input wire so that it now displays
VL, VC, or VR, as shown below. If the start of the graph is beyond the left edge of the screen, adjust
x position so you can see it. If it doesn’t start right on a peak, a valley or the centerline, push the
AT/NORM button, then adjust the blue LEVEL knob so it does. (Don't touch trig level again.)
- Record the peak voltage, being sure variable y amplitude (red knob) is fully
counterclockwise.
- Sketch the trace, paying attention to where in the cycle it begins at its left.
Next, switch the circuit element you just measured with one of the others by reconnecting them in
each other's places. Keep the scope’s black connected to the function generator’s black. Keep the
wires arranged the same way while switching the locations of R, L and C. Repeat the same
measurements. Repeat for the last of the three.
Get the instructor’s approval of your sketches before going on; there are often problems.
In your conclusion,
1. Comment on whether your measured and computed values for the three voltages agree with
each other if the measured values have a 10% uncertainty. (A typical tolerance when
components like these are manufactured.)
2. Comment on whether the voltages had the expected phase relationship:
a. Should VL lead or lag VR? Is this what you see?
b. Should VC lead or lag VR? Is this what you see?
PART TWO: Resonance
You will see if a circuit’s calculated resonant frequency matches the observed resonant frequency.
Use the same circuit from part I, except switch to a 47 Ω resistor. (Less resistance means more
current around the resonant frequency, making the peak stand out better on your graph.) Have the
scope measuring the voltage across the resistor. By I = V/R, the resistor's voltage is proportional to
the current, which is what we're really interested in.
Take data for a graph of resistor voltage as a function of frequency:
a) Find the frequency where the amplitude is largest. Record f from the dial on the function
generator. Record VR from the oscilloscope.
b) Record the same information for a frequency just 2 or 3 kHz above this, and again about 2 or
3 kHz below. We want this part of the graph to be clearly defined.
c) Record the same information at more widely spaced frequencies to fill out the range 100 Hz
to 100 000 Hz.
Plot the graph. Read the resonant frequency from it. Also, calculate the resonant frequency from L
and C. If your observed (graph) value has a 10% uncertainty, do these agree?
PHY 132
Report on Experiment 12: An AC Circuit
Part One:
R=
L=
Calculations:
C=
Measurements:
XL =
XC =
Z=
I=
VR =
VR =
VL =
VL =
VC =
VC =
Phase of voltage:
Part two: f
VR
_
a) ______________________
From graph, fR is _________________
b) ______________________
Calculate fR:
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c) ______________________
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