ENGINEERING-43
RL Series Circuits
Lab-17
Lab Data Sheet – ENGR-43 Lab-17
Lab Logistics
Experimenter: Bruce Mayer, PE
Recorder:
Date: 28Feb2008
Equipment Used (maker, model, and serial no. if available)
Fluke 8050A DMM; S/N 4630234
Tektronix TDS-340 Oscilloscope; S/N B015297
Tektonix CFG-250 Function/Signal Generator; S/N -3111
Knight K-240C LCR Meter, S/N 12001212
Directions
1. Check out:
 A DMM
 an Oscilloscope
 a Function/Signal Generator.
 Cables and Leads; include an dual alligator-clip lead
2. Go to the side counter, collect resistors, an inductor, “bread board”, and leads required to
construct the circuit shown in Figure 1.
3. See the Instructor to use the LCR meter to measure the actual value of the Inductance
 Use this Value and the DMM in DC-mode to complete Table I
4. Make the Measurements1 and Calculations needed to complete Table II
 All rms values are measured with the DMM
 Use the Scope’s MATH Ch1–Ch2 function to MEASURE Vcoil,pp
1
Refer to Lab-16 (RC AC-circuit) for instructions on how to set the frequency and amplitude of the signal
generator and how to make the requested measurements.
© Bruce Mayer, PE • Chabot College • 291220076 • Page 1

Use the scope MEASURE function to set the frequency and amplitude for the SignalGenerator for the listed frequencies.
 Use the Scope to Measure the Resistor, R2, Phase-Difference, , in Terms of TIME
using the scope CURSOR function as was described in Lab-16
5. Perform the Calculations needed to complete Table III
 Use the Signal Period and the Inductor Phase Time-Difference, , to calculate the
inductor phase ANGLE, , in degrees (°)
 Using measured values rms values calculate: |Zcoil|= Vcoil,rms/Irms
 Recall that Zcoil = Rw + jωL
 Now use the pythagorean formula to calculate L from |Zcoil|:
Zcoil  Rw2
2
L2calc 

2
Use the calculation and the LCR meter data to determine the % for the Inductor as
 L-% = 100x(LLCR – Lcalc)/LLCR
6. Use the Previous measurements and Calculations needed to complete Table IV
 The Impedance should be stated in POLAR Form,
7. Make the Measurements and Calculations needed to complete Table V
 All Voltage values Should be PHASORS, stated in polar form
 Determine The Phasor Value of Vcoil algebraically as the voltage-drop difference:
 Vcoil,calc1 = Vs – VR2,meas
 Determine The Phasor Value of Vcoil algebraically as the voltage-divider ratio:
 Vcoil,calc2 = Vs(Zcoil/Ztotal)
o Calculate this value of Zcoil using LLCR: Zcoil = Rw + jωLLCR
o Calculate Ztotal as: R2,DMM + Zcoil and Zcoil = Rw + jωLLCR
 Calculate VR2 using Voltage-Divider methods, utilizing the previously measured or
calculated values of the impedances
 VR2 = Vs(R2/Ztotal)
o Use the Ztotal value from just above
8. Make the Measurements and Calculations needed to complete Table VII
 Calculate the two Result Rations as
 RRc = (Vcoil,calc2)/(Vcoil,calc1)
 RRR2 = (VR2,calc)/(VR2,meas)
9. Make the Measurements and Calculations needed to complete Table VIII
 Measurements for Vcoil , Vs, VR2 and  are made with the OscilloScope
 Measure Vs using CH1
 Measure VR2 using CH2
 Use the Scope’s MATH Ch1–Ch2 function functions to measure Vcoil as:
o Vcoil = Vs – VR2
 Be sure to note whether  is LEADING or LAGGING
© Bruce Mayer, PE • Chabot College • 291220076 • Page 2


Calculate the Resistor Phase Angle using the standard method based on ratio of :T
 || = (360°)(/T) =
 Sign of based on LEAD or LAG
o LEAD → Positive 
o LAG → Negative 
The Resistor Phase Angle, , MUST stated in degrees (°)
10. Return all lab hardware to the “as-found” condition
Figure 1 • RL Series Circuit. Vs = 13 Vpp (Vamplitude = 6.5V), Vs = 6.5V0º, f per
the data-tables, L = 100mH (nominally), R2 = 1.7-2.3 k (2 k nominally)
© Bruce Mayer, PE • Chabot College • 291220076 • Page 3
Table I – Measure L The LCR-Meter, and measure Rw and R2 with the DMM in the DC mode
 Digital-Meter Actual-Values
R2 =
2.191 kΩ
Rw
L=
108.87 Ω
101.0 mH
Table II – Inductance Measurements
 Use the Scope’s MATH Ch1–Ch2 function to MEASURE Vcoil,pp
Frequency, f
T
VR2,pp
VS,rms
 for VR2
Vcoil,pp
Vcoil,rms
Icoil,rms
VR2,rms
1000 Hz
1.00 ms
46 μs lag
12.0 V
4.498 V
3.6 V
1.1970 V
1.8210 mA
4.134 V
3333 Hz
300 μs
37 μs lag
9.36 V
4.484 V
8.72 V
2.996 V
1.4330 mA
3.198 V
10000 Hz
99.83 μs
19.4 μs lag
4.56 V
4.497 V
12.32 V
4.230 V
0.7062 mA
1.5530 V
Table III – Inductance Calculations
Frequency, f
 for VR2
|Zcoil|
Lcalc
L-%
1000 Hz
-16.56°
657.3 Ω
103.17 mH
2.15%
3333 Hz
-44.4°
2091 Ω
99.70 mH
-1.29%
10000 Hz
-69.96°
5990 Ω
95.32 mH
-5.63%
© Bruce Mayer, PE • Chabot College • 291220076 • Page 4
Table IV – Series RL Impedance Calculation
Frequency, f
Lcalc
Rw
Zcoil
R2
Ztotal
1000 Hz
103.34 mH
108.87 Ω
657.3Ω80.5°
2.191 kΩ
2.390kΩ15.74°
3333 Hz
99.71 mH
108.87 Ω
2.091kΩ87.0°
2.191 kΩ
3.106kΩ42.23°
10000 Hz
95.32 mH
108.87 Ω
5.990kΩ89.0°
2.191 kΩ
6.415kΩ68.99°
Table V – Series RL Potential Measurements and Calculations

For Vs, VR2,meas, and Vcoil simply state in PHASOR form the measurements taken for Table VI
Frequency, f
Vs
VR2,meas
Vcoil,calc1
Vcoil,calc2
1000 Hz
6.5V0°
6.0V-16.56°
1.867V66.35
1.754V64.85°
5.97V-15.42°
3333 Hz
6.5V0°
4.68V-44.4°
4.55V46.05°
4.51V44.45°
4.56V-42.6°
10000 Hz
6.5V0°
2.28V-69.96°
6.11V20.53°
6.07V19.96°
2.11V-70.07°
Table VII – Series RL Potential Calculation Result Ratio

VR2,calc
State RR in POLAR for with proper units to at least 3 significant figures
Frequency, f
RRc = (Vcoil,calc2)/(Vcoil,calc1)
RRR2 = (VR2,calc)/(VR2,meas)
1000 Hz
0.9395-1.50°
0.99481.14°
3333 Hz
0.9912-1.60°
0.97441.80°
10000 Hz
1.001-1.58°
0.9253-0.381°

© Bruce Mayer, PE • Chabot College • 291220076 • Page 5
Table VIII – Series RL Potential Measurements Sweep
 Use the Scope’s MATH Ch1–Ch2 function to MEASURE Vcoil,pp
Frequency, f
Vs,pp
T
VR2,pp
Vcoil,pp
 for VR2
 for VR2
100 Hz
13V0º
9.972 ms
12.4
959 mV
90 μs Lag
-3.25°
400 Hz
13V0º
2.505 ms
12.32
1.759
46 μs Lag
-6.61°
1250 Hz
13V0º
800.4 μs
11.84
4.40
47 μs Lag
-21.14°
2.5 kHz
13V0º
400.5 μs
10.40
7.359
41 μs lag
-36.85°
8.0 kHz
13V0º
124.8 μs
5.44
11.84
24 μs lag
-69.23°
25.0 kHz
13V0º
40.07 μs
2.0
12.96
9.5 μs lag
-85.50°
80 kHz
13V0º
12.48 μs
416 mV
13.0
3.3 μs lag
-95.19°
NOTE: in Table VIII CALCULATE  for VR2 using the measured value of  for VR2
11. Use MATLAB or EXCEL to create two SemiLog plots of the data contained in Plot the Data Table VIII. 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: Vcoil,pp and VR2,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 →∞
Run Notes/Comments
SUPER FUN Lab, with WAY-COOL Calculations
EXAMPLE Hand-Calculations follow.
© Bruce Mayer, PE • Chabot College • 291220076 • Page 6
ENGR43 Lab-17 Voltage-Drop vs. Freqency for Series RL Circuit
14
12
Vcoil & Vr3 (Vpp)
10
8
Vr2
Vcoil
6
4
2
0
2
10
10
3
10
frequency (Hz)
© Bruce Mayer, PE • Chabot College • 291220076 • Page 7
4
10
5
ENGR43 Lab-17 Phase-Angle vs. Freqency for Series RL Circuit
0
-10
-20
Phase Angle.  (°)
-30
-40
-50
-60
-70
-80
-90
-100
2
10
10
3
10
4
10
5
frequency (Hz)
Print Date/Time = 29-May-16/04:00
© Bruce Mayer, PE • Chabot College • 291220076 • Page 8
MATLAB Code Used to Create the Previous Plots
% Bruce Mayer, PE * 21May10
% ENGR43 * Lab-17 RL Series Ckt Plots
% file = ENGR43_Lab17_RLckt_Plots_1005.m
%
% DATA from Lab-17 Sheet
f = [100
400
1250
2500
8000
25000
80000]
Vcoil = [0.959 1.759 4.40 7.359 11.84 12.96 13.0]
Vr2 = [12.4 12.32 11.84 10.40 5.44 2.00 0.416]
q = [-3.25 -6.61 -21.14 -36.85 -69.23 -85.5 -95.19]
%
% Vcoil & Vr2 plot
semilogx(f,Vr2, '--mo', f, Vcoil,':bs' ), grid, legend('Vr2','Vcoil'),
xlabel('frequency (Hz)'), ylabel('Vcoil & Vr3 (Vpp)'),...
title('ENGR43 Lab-17 Voltage-Drop vs. Freqency for Series RL Circuit')
disp('Showing Vcoil & Vr2 plot - hit ANY KEY to continue')
pause
%
disp('Showing Phase-Angle plot')
semilogx(f,q, '--mo' ), grid, xlabel('frequency (Hz)'), ylabel('Phase
Angle. \phi (°)'),title('ENGR43 Lab-17 Phase-Angle vs. Freqency for Series
RL Circuit')
© Bruce Mayer, PE • Chabot College • 291220076 • Page 9
© Bruce Mayer, PE • Chabot College • 291220076 • Page 10
© Bruce Mayer, PE • Chabot College • 291220076 • Page 11
© Bruce Mayer, PE • Chabot College • 291220076 • Page 12
© Bruce Mayer, PE • Chabot College • 291220076 • Page 13
© Bruce Mayer, PE • Chabot College • 291220076 • Page 14
Print Date/Time = 29-May-16/04:00
© Bruce Mayer, PE • Chabot College • 291220076 • Page 15