i ii iii electric circuits lab series rc circuits phase angle phase la

Question

I.
II.
III.
Electric Circuits Lab
Series RC Circuits: Phase Angle, Phase Lag, and Capacitors as Integrators
Part 1:
Objectives:
After completing this lab experiment using, you should be able to:
1. Understand the effect of frequency on capacitive reactance.
2. Measure the impedance of an RC circuit.
3. Measure the phase angle and phase lag of an RC circuit using the oscilloscope.
4. Draw the impedance and voltage phasor diagrams
5. Understand how a capacitor integrates current.
Parts List:
1. Resistor 1000, 1k, 6.8 k
2. Capacitors 0.1 µF, 0.01 µF
Procedures:
1. Connect the following circuit.
VS
1Vrms
1 kHz
R1
ww
1.0k
Figure 1: RC Circuit
1
C1
=0.1pF
2. Connect one DMM across the resistor and one DMM across the capacitor. Set both
DMM sto read AC voltage. Measure the voltage drop across each component. Record the
result in Table 1./n3. Use Ohm's law to calculate the current flowing through the resistor. Since the circuit in
Figure 1 is a series RC circuit, the same current will flow through the capacitor and the
resistor. Record the result in Table 1.
4. Calculate the capacitive reactance using Ohm's law. Record the result in Table 2.
Vc
Capacitive Reactance, Xc = I
Total current, I = R
5. Now, calculate the capacitive reactance value using the equation below. Record
the result in Table 1 under Computed Reactance, Xc.
Capacitive Reactance, Xc =
Frequency
(in Hz)
300
1k
Voltage across, R
Voltage across, C
Total Current, I
Capacitive Reactance, Xc
Computed Reactance, Xc
6. Adjust the function generator frequency following the steps in Table 2. Use the DMM to
measure the voltage across the resistor and the capacitor. Record your measurements
below.
1
2nfC
Table 1: Calculated and measured values
VR
Vc
(measured) (measured)
Capacitor C₁
2
VR
1 = R
Xe= I
(calculated) (calculated)
Vc
1
(2nfc)
(calculated)
Xc=/n3k
5k
7k
9k
11k
13k
15k
Table 2: Calculated and measured values
7. Plot the graph for Frequency vs. Vc.
(Use Excel or Word to Create the Plot)
Plot 1: Frequency vs. Vc
Part II:
8. Build the circuit shown in Figure 2.
1.5Vpk
500Hz
0
Vs
C1
HH
0.01 μF
R1
6.8kQ
Figure 2: Series RC Circuit
3
9. Set the source voltage amplitude to 1.5 V, and frequency to 500 Hz./n10. Connect Channel A of the oscilloscope across the resistor and measure the peak voltage
drop (VR). Record the result in Table 3.
11. Use Ohm's law to calculate the peak current flowing through the resistor. Because it is a
series circuit, the same current will flow through the capacitor. Record the result in Table
3.
VR
I
Total current = R
Vc
Xc
Z₁
Table 3: Calculated and measured values
12. Connect Channel B of the oscilloscope across the capacitor and measure the peak
voltage drop (Vc). Record the value in Table 3.
13. Calculate the capacitive reactance using Ohm's law. Record the result in Table 3.
Vc
Capacitive Reactance Xc = 7
e
Vs
Total Impedance (ZT) = Ť
14. Now, calculate the total impedance (Z₁) value using the equation below. Record the
result in Table 3.
15. Calculate the phase angle between VR and Vs using the formula below. Record the result
in Table 3. Also, record this value in Table 4 under Phase Angle calculated value.
Phase angle, 8 = -tan-¹ (*)
Part III: Phase Angle and Phase Lag Measurement
Phase Angle
16. Connect Channel A of the oscilloscope across the resistor and Channel B of the
oscilloscope across the function generator and run the simulation.
17. The waveforms should look like the ones shown in Figure 4./nMAAAA
Vs
VR
Figure 4: Vs and VR waveforms
18. Obtain a stable display showing a couple of cycles for Channel B (which is showing Vs)
and disable Channel A by setting it to 0.
19. Measure the time period (T) of the source voltage. Record the result in Table 4 below.
(Use the cursors to measure the period (on the scope it will show as T2-T1). Remember
that the period is the time taken to complete one cycle). See Figure 5.
Figure 5: Measuring time period (T)
5/nType of Angle
Phase angle 8
Phase Lag
Measured
Period (T)
Time difference Measured
(At)
Angle
Table 4: Phase angle and phase lag measurements
20. Now set the oscilloscope to view both the channels.
21. Adjust the amplitude of the signals using Channel A and Channel B V/Div scale until both
channels appear to have the same amplitude as seen on the scope face. (as close as
possible)
Phase Lag
22. Spread the signals horizontally using the Timebase (Sec/Div) control until both signals are
just visible across the screen as shown below.
Calculated
Angle
23. Measure the time duration between the two signals (At) and record the result in Table 4
above. (Use cursors as shown below in Figure 6)
Figure 6: Measuring the time difference
24. Calculate the phase angle using the formula below and record the result in Table 4.
Phase angle, 8 = (At/T)* 360°/nlag circuit will lag the input voltage.
1.5Vpk
~500Hz
0"
Vs
R2
6.8kQ
C2
=0.01 μF
Figure 7: RC Lag Circuit
XSC2
26. Calculate the phase lag using the equation below. Notice the similarity to the equation for
the phase angle. The phase lag angle and phase angle of an RC circuit are
complementary angles. (Their sum is 90°.) Use R and Xc values from Table 3.
Phase Lag, ø = tan-¹)
27. Measure the time period (T) of the source voltage (as in Step 19). Record this value in
Table 4.
28. Now set the oscilloscope to view both the channels.
29. Adjust the amplitude of the signals using Channel A and Channel B V/Div scale until both
channels appear to have the same amplitude as seen on the scope face. (as close as
possible)
7
30. Spread the signals horizontally using the Timebase (Sec/Div) control until both signals are
just visible across the screen as shown in Figure 6.
31. Measure the time duration between the two signals (At) and record the result in Table 4
above.
32. Calculate the phase lag using the formula below and record the result in Table 4.
Phase lag, Ø = (At/T) * 360°/n33. Plot the Voltage and Impedance Phasor Diagrams. Clearly indicate the phase angle and
the phase lag. Measure the peak voltages for VR and Vc with the oscilloscope.
(Use Excel or Word to create diagrams)
Plot 2(a) Impedance Phasor
Plot 2(b) Voltage Phasor
Part IV: The Capacitor Integrates Current
34. Construct the following RC circuit in Multisim. Set the clock voltage source to 10 kHz,
10V, 50% duty cycle./nru
ru
V1
10kHz
10V
V1
10kHz
10V
Figure 9. Integrator Circuit
35. Connect Channel A across the resistor and Channel B across the capacitor. (Note:
change one or both trace colors to better observe the two signals)
R1
3kQ
R1
mw
3kQ
C1
5.6μF
C1
5.6μF
Figure 9a. Integrator Circuit with Oscilloscope Connections
ET
36. Run the simulation. Your signals should look like the example in Figure 9b./nOscilloscope-XSC1
T2
T2-T1
VR
Vc
Time
164.481 ms
164.481 ms
0.000 s
Timebase
Scale: 20 us/Div
X pos.(Div): 0
Y/T Add B/A A/B
Channel A
-4.999 V
-4.999 V
0.000 V
Channel B
-1.675 mV
-1.675 mV
0.000 V
Channel A
Scale: 2 V/Div
Y pos.(Div): 0
AC O DC
Figure 9b: Capacitor as an integrator waveforms
Channel B
Scale: 5 mV/Div
Y pos.(Div): 0
OAC 0 DC-
v(t)
>= ²1 [₁
v(t) = ½ ju(t)dr
{=C
37. Channel A will show the voltage across the resistor. This signal can be used to find the
circuit current using Ohm's law.
38. Channel B shows the voltage across the capacitor. Show that this signal satisfies the
following equation. We will do this in intervals in the following steps.
dv
dt
i(t)dr
Reverse
=
- 1/1(1)
Save
t(t)dt + +
Ext. trigger
Trigger
Edge: A B Ext
Level: 0
O Single Normal Auto None
t(r)dr/nT2
T2-T1
39. Refer to Figure 10 to answer the following questions.
Oscilloscope-XSC1
Time
164.100 ms
164.150 ms
50.001 us
v(0) = 1 ju(r)dr
v(t):
1) = ²½ [167)ar = √ [ 16
[1(r)dr
Timebase
Scale: 20 us/Div
X pos.(Div): 0
Y/T Add B/A A/B
Channel A
-1.993 V
1.992 V
3.985 V
Channel A
Scale: 2 V/Div
Y pos.(Div): 0
AC O DC
Channel B
-7.425 mV
14.882 mV
Channel B
Scale: 5 mV/Div
Y pos.(Div): 0
O AC O DC
Figure 10: Integrator values, 0 to 50 µs
i(t):
11
1(T)dt + v(0)
t=50μS
=
mVys
a. The signal has a period of 100 us. Write the equation for the circuit current on the
interval 0 to 50 us. On the interval of 0 to 50 µs, va(t) is constant so the current will
be constant as well.
VR(t)
R
Reverse
Save
Ext. trigger
Trigger
Edge: A B Ext
Level: 0
V
Single Normal Auto None/nb. Write the equation for the voltage across the capacitor by solving the integral. You
will need to read the value vc(0) from Figure 10.
50 μ
v(t) = [1(x)dx+v(0)
c. Confirm your equation by predicting the value of vc(50 µs).
d. Read the value of vc(50 us) from Figure 10.
40. Refer to Figure 11 to answer the following questions.
Oscilloscope-XSC1
T2
T2-T1
t=50μs
Time
164.400 ms
164.450 ms
50.001 us
Timebase
Scale: 20 us/Div
X pos.(Div): 0
Y/T Add B/A A/B
Channel A
-1.993 V
1.992 V
3.985 V
Channel A
Scale: 2 V/Div
Y pos.(Div): 0
AC O DC
t=100μs
12
Channel B
-7.424 mV
7.457 mV
14.882 mV
Channel B
Scale: 5 mV/Div
Y pos.(Div): 0
AC 0 DC
Figure 11: Integrator values, 50 to 100 μs
X
Ext. trigger
Reverse
Save
Trigger
Edge:
A B Ext
Level:
0
V
Single Normal Auto None/na. The signal has a period of 100 us. Write the equation for the circuit current on the
interval 50 µs to 100 µs. On the interval of 50 to 100 μs, vr(t) is constant so the
current will be constant as well.
i(t) =
VR(t)
R
b. Write the equation for the voltage across the capacitor by solving the integral. You
will need to read the value vc(50) from Figure 11.
v(t) = 11(x) + (50)
50 μs
c. Confirm your equation by predicting the value of vc(100 µs).
d. Read the value of vc(100 us) from Figure 11.