ENGR 12L
Experiment 12: AC Circuit Measurements
Name(s)___________________
Oscilloscope vs DMM, Magnitude vs RMS
Oscilloscopes measure instantaneous voltages only and can measure amplitude (Xm), period and frequency. They can
also be used to measure the phase angle between two voltage waveforms.
Digital Multimeters (DMM) can only measure RMS, but can measure voltages and currents.
We are going to use a combination of scopes and meters to characterize the impedance of two circuits: an RC and series
RLC.
Materials:
Oscilloscope
Function Generator
0.1 uF capacitor
360 Ohm Resistor
Measured___________
Measured___________
PART 1 Series RC circuit
Function generator Vs = 14 V pp (amplitude = 7V)
Frequency = 1000 Hz (to begin)
R = 360 Ω
C = 100 nF (0.1 µF) nominally
Fig 1: Series R-C circuit
1) Use a DMM multimeter to measure R and C before you build the circuit (enter values above)
2) Build the circuit shown above
3) Set the function generator to 1kHz 14Vp-p Sinewave and connect the oscilloscope Ch1 across Vs as shown in the
schematic.
4) Use the scope to verify the correct frequency, and amplitude of the source waveform (make sure it's a
sinewave). Freq= _____________ Period T = __________________ Amplitude = ________________Vpp__
5) Use the DMM to measure Vs_rms. Record these measurements as well as the calculated Vrms based on Vpp.
6) In order to measure current, we'll measure VR and divide by R (Ohm's law). In order to measure VR we'll just
use Ch2 of the scope.
7) Complete the table below comparing Vpp values, RMS calculated (Vm/√2) and RMS measured from DMM
8) For IR just take VR and divide by R for all three rows
Table I Voltage measurements at 1000 Hz.
Value Determination
Vs
VR
IR (= VR /R)
Scope Vpp
RMS Calc
DMM RMS
9) We assume 𝜃𝑣 = 0 , (the phase angle of our voltage source), since we are making the voltage source Vs our
reference. Since VR is directly proportional to IR, we can measure the phase of the current source relative to Vs
by measuring the phase offset between VS .and VR. Use the CURSOR, VBARS buttons to measure the time offset 
between the sinewave peaks on VR and VS. Scale this time offset  by 360/T to get phase. The sign of the phase
angle (𝜃𝑖 ) should be positive if the VR waveform peaks to the left of the VS waveform. This is an example of how
the current "leads" the voltage and is the norm for capacitive circuits. (Note: if we were doing power
calculations the angular expression 𝜃𝑣 − 𝜃𝑖 would be a negative number when the current leads the voltage).
Summarizing,
𝜃𝑖 = 𝜏
360𝑜
𝑇
and should be positive if the current peaks before the voltage
10) Complete Table II of phase measurements at 1000 Hz
Table II Current phase measurement at 1000 Hz
Frequency, f
, ms
T, ms
𝜃𝑖 , degrees
1000 Hz
11) We now have all of the information needed to compute the impedance of our RC circuit in two ways: theoretical
and experimental.
12) Find Zeq for the RC network as seen by the voltage source Vs at f = 1000 Hz (remember w = 2*pi*f !). Use the R
and C values from your multimeter measurements:
theoretical Zeq = R - j/(wC)
=
_____________________________
13) Find Zeq for the RC network by dividing the phasor Vs (angle 0) by the phasor IR (use the phase angle 𝜃𝑖 for IR
you calculated in Table II) and convert the result to rectangular form. Since we are dividing you can use either
the peak-to-peak values or the rms values for the amplitude of the phasors:
experimental Zeq = Vs/IR = __________________________ (polar) = ___________________________ (rect)
14) Now repeat these measurements at two additional frequencies:
Frequency, f
Vs_pp
1000 Hz
14V
4500 Hz
14V
10000 Hz
14V
Vr_pp
Ir_pp
T
 for VR
𝜃𝑖
Zeq theory
Zeq
exprmnt