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Physics 481
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Experiment 1
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LINEAR CIRCUITS
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Experiment 1 - Linear Circuits
This experiment is designed for getting a hands-on experience with simple linear
circuits. The project is intended to cover both building and analysis of such circuits, as
well as usage of two measuring devices – digital millimeters and oscilloscopes. The
circuits covered in this project will utilize only passive electronic components: resistors,
capacitors, and inductors, covering typical properties of RC, LC, and RLC circuits. The
experiment will also address the effects of measuring devices on a circuit.
Part 1. Effects of Measuring Instruments on Results
Voltmeter and Voltage Divider
One of the first things to be aware of in
electronics is that the very instruments that are used
can have an effect on the measurements that are
being taken. Consider the input characteristics of the
DMM. Set up a simple voltage divider consisting of
two resistors of equal value on the breadboard as in
Fig. 1.
R1
+
5V
R2
Figure 1: Voltage Divider.
Check the actual resistor values with the DMM to be sure. Make a note if the measured
values are within the tolerance from the ones specified.
Now use the 5 V power supply on the breadboard to apply a voltage to the divider. Use
the DMM to measure the voltage across both resistors as well as each resistor separately.
Start with 10k resistors. Check if the voltage drops across each resistor sum to the drop
across both resistors in series.
Repeat the process with 100k resistors and finally 1M resistors, each time checking
the sum of voltage drops with respect to the total potential difference for two resistors in
series. Note at which conditions the internal resistance of the meter is most evident.
With the data obtained on voltage divider with the 1M resistors calculate the internal
resistance of the DMM itself. Assume that this DMM resistance alters the effective
resistance of the divider; thus causing the change in voltage from the expected results.
Make a generalized conclusion about ideal characteristics for voltmeters and the effects
of real voltmeters on circuits
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Ammeter and Current Divider
Construct a current divider on the breadboard. Use
two equal resistors in parallel driven by the 5 volt
supply as in Fig. 2. Use one DMM to measure the
total current through both resistors and another
DMM to measure the current through one resistor.
+
5V
R1
R2
Figure 2: Current Divider.
Start your setup with the 10k resistors and
measure the total and the branch currents
(remember ammeters are to be connected in series). Check the “junction rule”.
Repeat the measurements with the 1k resistors (or 1.1k as per availability), and then
51  resistors. Explain for which setup the effects of ammeter on the circuit are most
evident. Estimate the ammeter internal resistance.
Finally, construct a simple series circuit with a 5 V power source, a 51  resistor and one
DMM in the “200 mA” mode. Use the second DMM to measure the voltage across the
first DMM. Calculate the resistance of the first DMM. Check if your result can explain
the observations from the current divider?
Make a generalized conclusion about ideal characteristics for ammeters and the effects of
real ammeters on circuits
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Part 2. RC-Circuits
RC Integrator
x
Construct the circuit shown in Fig. 3 and
explore the properties of RC-Integrator
circuit. Drive the circuit with a 500 Hz
square wave and observe the output with
oscilloscope. Explain if your result
confirms the idea of this being an
integrating circuit.
Using the R and C specifications as in the
figure, confirm that the circuit satisfies the
necessary criteria of RC-integrator.
R1 =1M
500 Hz
Square Wave
Oscillo
scope
C=0.01uF
Figure 3: RC-Integrator Circuit
Next drive the circuit with a triangle wave as an input. Sketch the output, and explain your
results in context of integrator circuits.
RC Differentiator
C=200pF
By interchanging the resistor and
capacitor and adjusting the values the
RC
integrator
circuit
can
be
transformed into an RC differentiator as
shown in Fig. 4.
Using the R and C specifications as in
the figure, confirm that the circuit
satisfies the necessary criteria for RCdifferentiator.
x
100 kHz
Saw Tooth Wave
Oscillo
scope
R1 =100
Figure 4: RC-Differentiator Circuit
The operational (transfer) function of the circuit is now that of a differentiator. Drive the
circuit with a 100 kHz triangle wave. Sketch and explain the result.
Repeat with a square wave.
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Part 3. RLC-Circuit
Ringing
Construct the RLC circuit as shown in Fig.
5. Use the element specifications as in the
Figure. The initial resistance value for R1 to
be 10 k. Use a square wave with the
frequency f=1 kHz as the input for the
circuit. Observe the output on your
oscilloscope. You should see the classic
"ringing" response - an example of an
“under-damped oscillation”.
R1
C=0.01uF
L=1000
uH
Square Wave
G
Figure 5: Ringing the RLC-circuit.
The general solution for this circuit could be written as follows:
1
2
2
Vr(t) = V0 e-αtcos( t), where α =
, w = wr - a ,  r 
2 RC
1
LC
Measure the frequency of the ringing using the oscilloscope. Compare the result with the
resonant frequency ωr
Use the peaks of the ringing signal to plot out the e-αt form. Determine  graphically, by
using semi-log axis in plotting. Compare this result with the calculated value.
Resonant Circuit
Construct a circuit as shown in Fig. 6. Show
that the square of the resonant frequency is
given by 1/LC. Run your generator through
several ranges to find the peak output.
Determine the resonant frequency r and
compare this value with the expected resonant
frequency.
Next, find the frequencies 1 and 2 for which
the output reaches the value of 0.707Vr. Use
the necessary information to calculate the
selectivity r/BW, where BW stands for
bandwidth, BW= 2-1
R1=100k
L=10 mH
+
V
V0cos(t)
C=0.01uF
-
Figure 6: Resonant Circuit.
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