ENGINEERING-43
RC Series Circuits
Lab-13
Lab Data Sheet – ENGR-43 Lab-13
Lab Logistics
Experimenter:
Recorder:
Date:
Equipment Used (maker, model, and serial no. if available)
Directions
1. Check out
 a DMM
 an oscilloscope
 a Signal/Function Generator.
 Cables and Leads
2. Go to the side counter, collect resistors, a capacitor, “bread board”, and leads required to
construct the circuit shown in Figure 1. See also Figure 2.
3. See the Instructor to use the LCR meter to measure the actual value of the Capacitor
4. Use the DMM to measure the actual value of the Resistor
© Bruce Mayer, PE • Chabot College • 291211011 • Page 1
Figure 1 • RC Series Circuit.


Vs = 14 Vpp (Vamplitude = 7V) or
Vs = 7V0º

f = per Table I or Table IV.

R = 350-750 Ω (470 Ω nominally).

C = 100 nF (0.1 µF) nominally.
Digital-Meter Actual-Values
R=
C=
5. Make the Measurements and Calculations needed to complete Table I.
 Reveal the Vs-GND signal on the Scope
 Connect CHANNEL-1 between the Vs and GND nodes for the circuit shown in
Figure 1 (measures Vs-GND)
 Press the CH1 Button to bring the signal onto the display
 Set up the waveform for each frequency using the TDS340 Oscope
 Set the Frequency, f: [MEASURE Menu] → [Frequency side menu-1, button-2].
See Figure 3.
 Set the Peak-to-Peak Amplitude, Vpp: [MEASURE Menu] → [Pk-Pk side menu3, button-3]
 Confirm the Period, T : [MEASURE Menu] → [Period side menu-1, button-1]
 Reveal the Vc-GND signal on the Scope
 Connect CHANNEL-2 between R and C (measures Vc-GND)
 Press the CH2 Button to bring the signal onto the display
o Both the CH1 and CH2 traces should be simultaneously displayed
 Use the Scope to Measure the Capacitor Phase-Difference, , in Terms of TIME
© Bruce Mayer, PE • Chabot College • 291211011 • Page 2



Expand the SEC/DIV scale on the scope to make a maximally precise
measurement of the time-based phase difference
o See the Instructor if you are unsure about this procedure
 Measure  using the cursors – See Figure 4 and Figure 5.
o Activate the Vertical-Bar cursors:
[CURSOR button] → [Side Menu = V Bars]
o Use the SELECT button and the GENERAL PURPOSE knob to position
the Left cursor at the peak of the left-most trace.
o Use the SELECT button and the GENERAL PURPOSE knob to position
the Right cursor at the peak of the left-most trace.
o Read the “Δ” measurement in the upper-left corner of the display
 Be Sure to Note if  LEADS or LAGS the source which is DEFINED to have
ZERO phase angle
 Measure Vc,pp using the cursors
o Activate the Horizontal-Bar cursors:
[CURSOR button] → [Side Menu = H Bars]
o Use the SELECT button and the GENERAL PURPOSE knob to position
the top cursor at the peak of the CH2 trace.
o Use the SELECT button and the GENERAL PURPOSE knob to position
the Bottom cursor at the trough of the CH2 trace.
o Read the “Δ” measurement in the upper-left corner of the display
Use The DMM in “TRUE RMS” mode to measure the rms values for V & I
Be sure readjust the amplitude every time the frequency is changed
Table I – Capacitance Measurements
Frequency, f
T
 for Vc
Vc,pp
Vc,rms
Ic,rms
1000 Hz
3333 Hz
10000 Hz
6. Perform the Calculations needed to complete Table II
 Use the Signal Period and the Capacitor Phase-Difference Time to calculate the
capacitor phase ANGLE, , in DEGREES (°) relative to the base-line value for Vs:
   
LEAD 
360
 sec 
T sec 
 LAG 



Using measured values calculate: |XC| = Vrms/Irms
From measured Vrms & Irms values Calculate C from the expression for XC
 |XC| = Vrms/Irms = 1/(C)
Use the calculation and the LCR meter data to determine the % for the Capacitor as
 C-% = 100x(Ccalc – CLCR)/CLCR
© Bruce Mayer, PE • Chabot College • 291211011 • Page 3
Table II – Capacitance Calculations
 for Vc
Frequency, f
|XC|
Ccalc
C-%
1000 Hz
3333 Hz
10000 Hz
7. Use the Digital-Meter Actual Values for R & C, and the rms & scope measurements to
complete Table III. Specifically CALCULATE the
 Capacitor impedance, Zc (specify in RECTANGULAR form):
Zc 

1
j
1
1 


 j
 jX c , LCR  Note that X c 

jC C
C
C 

Single-loop phasor circuit current Ic using Ohm’s law (specify Ic in POLAR form):
Ic 

Vs
Vs

Z series R  Z c
Single-loop phasor Voltage across the Capacitor, Vc, by the Voltage Divider method
(specify Vc in POLAR form):
Vc  Vs
Zc
Zc
 Vs
Z series
R  Zc

All Phase Angles MUST stated in degrees (°)

To Calculate the Δ%’s, Let “Q” = Ic or Vc, and “Brms“ = Irms or Vrms, then:
Q% 
Q

2  Brms
Brms
Table III – Impedance-Based Calculations
Frequency, f
Zc
Ic
Vc
1000 Hz
3333 Hz
10000 Hz
© Bruce Mayer, PE • Chabot College • 291211011 • Page 4
Ic-%
Vc-%
8. Make the Measurements and Calculations needed to complete Table IV
 Use the Scope to measure Vc,pp
 Use the Scope MATH menu MEASURE DIRECTLY VR,pp
 Press the MATH button
o On the side menu press button-2 to activate the Ch1-Ch2 measurement
 With the MATH WaveForm selected Press the MEASURE Button
o On the side menu press the button needed to activate the Pk-Pk
function. See Figure 6.
 Use the Scope CURSOR function to measure the TIME-based phase difference, , for
Vc as was done in step 5
 Expand the SEC/DIV scale on the scope to make a maximally precise
measurement of the time-based phase difference
 Be sure to note whether is  LEADING or LAGGING
 Using  determine the Capacitor Phase Angle  in DEGREES (°)
Table IV – Series RC Potential Measurements Sweep
Frequency, f
Vs,pp
100 Hz
14V0º
400 Hz
14V0º
1250 Hz
14V0º
2.5 kHz
14V0º
8.0 kHz
14V0º
25.0 kHz
14V0º
80 kHz
14V0º
Vc,pp
VR,pp
 for Vc
 for Vc
.
Note: Low frequencies such as 100Hz can be difficult to measure on older scopes
9. Use MATLAB or EXCEL to create two SemiLog plots of the data contained in Plot the Data
Table IV. In both plots the frequency, f, will be plotted on the Logarithmic scale
 Plot-1
 Independent variable = log(f)
 TWO dependent variables on the same plot: Vc,pp and VR,pp
 Plot-2
 Independent variable = log(f)
 Dependent variable = 
 Attach both plots to this lab report
 ANALYZE the trends shown in the plots, and comment on the physical CAUSE of the
observed trends
 HINT: Consider the Behavior of the Circuit in these extreme cases
o →0
o →∞
© Bruce Mayer, PE • Chabot College • 291211011 • Page 5
10. Return all lab hardware to the “as-found” condition
Figure 2 • Connection of the circuit components and instrumentation.
© Bruce Mayer, PE • Chabot College • 291211011 • Page 6
Figure 3 • Using the TDS430 MEASURE functions to set the frequency of the CGF250.
© Bruce Mayer, PE • Chabot College • 291211011 • Page 7
Figure 4 • Using the TDS430 CURSOR function to measure the sign time difference, . In
this case the space between the traces must be Expanded using the HORIZONTAL
SCALE to improve the measurement accuracy.
© Bruce Mayer, PE • Chabot College • 291211011 • Page 8
Figure 5 • Using the TDS430 CURSOR function to measure the sign time difference, .
When compared to Figure 4 note how the horizontal scale has been expanded from 50
μs to 25 μs to increase the peak-to-peak distance to improve the measurement
accuracy. See Figure 5.
© Bruce Mayer, PE • Chabot College • 291211011 • Page 9
Figure 6 • Using the TDS430 MEASURE functions measure directly the Ch1–Ch2 signal
difference.
Run Notes/Comments
Print Date/Time = 29-May-16/04:00
© Bruce Mayer, PE • Chabot College • 291211011 • Page 10