Download PHYS 2426 – Engineering Physics II

6/29/2017
Series LRC Circuit
Amplitude and Phase
Materials
Capacitor, 0.068μF
AC/DC Electronics Lab Pasco w/ Inductor
8.4mH on board
BNC T in Adapter/Connector Parts Box
Function Generator Model 4017A
Cable, BNC/Alligator
LCR Meter Extech Model 380193
Cable, BNC/BNC
Oscilloscope Model TDS 1002B
Cable, Passive BNC/Probe (2)
Resistor, 560Ω
Introduction
In this lab we will investigate the series LRC circuit. We will construct a series LRC
circuit and apply an AC signal. We will measure the amplitude of the potential
differences across each of the elements in the circuit and the potential across the entire
circuit and explore the relationships between them.
Procedure
1. Setup
We will use the circuit board in the Pasco AC/DC Electronics Lab to construct
the RLC series circuit shown in Figure 1.
Figure 1
A
Capacitor
0.068μF
B
Inductor
8.4mH
Function
Generator
C
Resistor
560ohm
D
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2. To make the circuit we will use a .068 μF capacitor, a 560 Ω resistor, and the
8.4 mH inductor mounted on the Pasco circuit board. Use the LCR meter to
measure the values of each component before assembling the circuit. You can
switch between capacitance, resistance, and inductance on the LCR meter by
pressing the LCR button. Record the values.
R  ______________
C  ______________
L  ______________
3. Use the spring clips to connect the components in the order shown in the
circuit schematic. (The instructions in this lab will be written assuming you
connected the components in the order shown.)
4. Place the BNC/T on the output of the function generator.
5. Use the BNC/Alligator cable to connect the output of the function generator
across the circuit as shown in the schematic (Note: Red to point A and black
to point D. Black is ground reference.)
6. Connect the output of the function generator to channel 1 of the oscilloscope
with the BNC cable.
7. Turn on the function generator, verify that it is in sine wave mode, and set the
frequency to 7.5 kHz.
8. Turn the oscilloscope on and allow it to go through startup sequence. Press
the ‘AUTO SET’ button. Press ‘MEASURE.’
9. Adjust the amplitude with the ‘OUTPUT LEVEL’ knob on the function
generator so that the oscilloscope indicates 5 V. (Get as close as you can.)
10. Press the Cursor button. Select the ‘Time’ mode in the ‘Type’ menu and then
measure and record the frequency of the input sine wave. In this mode the
two knobs marked ‘POSITION’ will move the cursors. Place them across a
single cycle to read a value on the left of the screen. (Alternatively: The
frequency should automatically be indicated at the lower right of the screen.
This will show how well you spotted your cursors.)
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11. Switch the cursors to ‘Voltage’ mode and measure the peak-to-peak amplitude
of the sine wave. The amplitude is ½ the peak to peak amplitude. Be sure to
include appropriate units below and everywhere else.
Input Sine Wave Channel 1
Vamplitude  __________________
Frequency  __________________
Q1) What is the RMS amplitude of the input sine wave?
Vrms  __________________
Next, we are going to measure the amplitude of the potential across each of the elements
and determine the phase relationships.
12. Remove the BNC cable from Channel 1 and replace it with a BNC/probe. Put
a BNC/probe in Channel 2. The oscilloscope probes have a switch on them
labeled 1x – 10x. Verify that both of the oscilloscope probes are set to the 1x
position.
13. Connect the BNC/probe from Channel 1 across the circuit parallel to the leads
from the function generator (AD.) The alligator clip is connected to
ground, so it needs to be connected to the resistor with the black lead. Press
the Auto Set button.
Q2) Measure and record the amplitude as well as RMS potential.
Vamplitude  ___________________
Vrms  ___________________
Q3) How do your answers to Q2 compare to what you measured for the output of the
function generator? Explain why this is the case.
14. Now connect the BNC/probe from Channel 2 across the resistor (CD.) The
polarity is important here. Connect the hook to the resistor on the side where
it connects to the inductor (point C.) Clip the alligator clip to the side of the
resistor connected to the black lead running to the function generator (point
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D.) Push ‘AUTO SET.’ You should see a screen with a trace labeled ‘1’ and
a trace labeled ‘2.’
We now wish to make several measurements.
Q4) Measure the amplitude of the potential difference across the resistor and determine
the RMS potential. This can be facilitated by using the measurement cursors.
resistor
Vamplitude
 ___________________
resistor
Vrms
 ____________________
(You can compare your calculated value with the direct readout on the oscilloscope.
We have a technical issue with the use of the oscilloscope that we have to deal with. The
oscilloscope acts like an AC voltmeter except that is always measures the potential
between the probe and a reference point of the earth (usually referred to as ground). We
have to take this into account in using the oscilloscope or we will simply short out our
signal. We will deal with this issue by using the SUBTRACT feature of the oscilloscope.
15. In a similar manner to how you just connected the probe across the resistor,
connect the probe connected to Channel 1 at a point between the inductor and
capacitor. (BD) Connect the alligator clip at the same place as the alligator
clip for the other probe is connected. The oscilloscope should now display
signals for both channels. If only one shows, press the CH 1 button so that the
second trace shows as well.
The oscilloscope should now display two signals. One is the potential difference across
the resistor on CH 2 and the other is the potential difference across the combination of the
inductor and the resistor on CH 1.
Q4) If we subtract the signal on CH 2 from CH 1, what do we obtain?
16. Make sure that the vertical sensitivity for both channels is set to the same
value.
17. Press the Math Menu button (located between the CH1 and CH 2 buttons).
Choose ‘–‘ as the operation and make sure that ‘CH1 – CH2’ is highlighted.
The scope will now display three traces. At the left of the screen, they are
labeled with a ‘1’ for CH1, a ‘2’ for CH2 and the difference is labeled with an
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‘M.’ You may need to adjust the vertical position so all three traces are
shown.
18. To improve accuracy, adjust the horizontal sensitivity so that a little over 1
cycle of the sine waves is displayed.
Q5) Measure the amplitude of the potential difference across the inductor and determine
the RMS potential. This can be facilitated by using the measurement cursors. To use the
measurement cursors again press the Cursor button and set to the ‘Voltage’ mode.
L
Vamplitude
 ___________________
L
Vrms
 ______________________
CH2 shows the potential difference across the resistor and the difference shows the
potential difference across the inductor.
Q6) Are the two signals in phase?
19. You can now use the cursor set in the ‘Time’ mode to find the phase
difference. The phase difference, in degrees, is defined as
t
 360
T
Where
 
T  period and
t is the time between a peak in the signal across the inductor and the
nearest peak in the signal across the resistor. Alternatively, you could
multiply by 2π to give the phase difference in radians.
Q7) Determine the phase difference between VL and VR by measuring t and T. Set the
cursors in ‘Time’ mode and measure these two values.
Q8) Which peak, VL or VR , is to the left?
The peak to the left we say leads the other peak.
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Q9) Does VL lead VR or is it the other way around?
We now want to make the same set of measurements between the potential difference
across the capacitor, VC and the potential difference across the resistor, VR . It turns out
that the easiest way to do this is to rebuild the circuit reversing the positions of C and L
shown in Figure 1.
20. Figure 2 shows how to switch the positions of the inductor and the capacitor
in the circuit to repeat the same measurements that you made for the inductor
with the capacitor.
Figure 2
A
Inductor
8.4mH
B
Function
Generator
Capacitor
0.068μF
C
Resistor
560ohm
D
Q10) Measure the amplitude of the potential difference across the capacitor and
determine the RMS potential. This can be facilitated by using the measurement cursors.
To use the measurement cursors again press the Cursor button.
C
Vamplitude
 ___________________
C
Vrms
 ______________________
Q11) Determine the phase difference between VC and VR by measuring t and T.
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Q12) Which peak, VC or VR , is to the left?
Q13) Does VC lead VR or is it the other way around?
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We can display the potentials and their phases by using a phasor diagram. In a phasor
diagram we treat the potentials like they’re components of a vector. VR is taken to be the
x component. Since VL is 90° ahead of VR it is taken as a positive y-component and VC
trailing by 90° is taken as a negative y-component.
Q14. Draw a scale phasor diagram for the RMS potentials that you measured in this lab.
Q15. Use the usual rules for vector math to find the magnitude of the RMS potential
across the entire circuit, i.e. VR  VL  VC .
Q16) The angle between the net potential and VR is called the phase angle. Determine
the phase angle from your measured values.
We can use phasors to derive general expressions for the potential and the phase.
VL
Veffective

VR
VC
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Q17) For the phasor diagram shown above, find expressions for Veffective and  in terms
of VR , VL , and VC .
We can express the potentials in terms of the current flowing in the circuit, viz. VR  iR ,
VC  iX C and VL  iX L .
Q18) Substitute the expressions given above into your answers for Q17 and show that


you obtain Veffective  iZ and tan   X L  X C .
R
Q19) Determine the impedance, rms current, and the phase for the circuit you have
constructed.
Connect the probe on CH 1 across all three elements and connect the probe on CH2
across the resistor. (You can turn off the math if it makes things too cluttered.)
Q20) Determine the phase difference between the two signals.
Q21) Determine the % difference between your measured phase and the phase you
determined in Q19).
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Q22) Use the expressions VR  iR , VC  iX C and VL  iX L to determine the RMS
amplitude across each component.
Q23) Determine the % differences between the values you determined in Q22 and the
corresponding values you measured earlier in the lab.
Q24) Based on your experience with this lab, how accurately can you model a series
LRC circuit? Justify your answer.
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