POLYTECHNIC UNIVERSITY
Electrical Engineering Department
EE SOPHOMORE LABORATORY
Experiment 2
DC circuits and network theorems
Modified for Physics 18, Brooklyn College
___________________________________________________________________________________________
I. Overview of Experiment
In this experiment you will verify experimentally the basic properties of resistive circuits.
Specifically, the major objectives are to
a) Verify Kirchhoff’s Current Law (also known as the junction rule and abbreviated here
as KCL), Kirchhoff’s Voltage Law (also known as the loop rule and abbreviated here as
KVL), and Ohm's law.
b) Experiment with the concepts of linearity and superposition.
c) Verify Thevenin's theorem by measuring the v-i characteristics of a circuit at a pair of
terminals.
d) Demonstrate the theorem of maximum power transfer.
II. Equipment Required
2 DC power supplies ( Range 0-20V )
1 Digital Multimeter
1 Protoboard
1 4.7kΩ resistor
2 10kΩ resistors
2 2kΩ resistors
1 Decade resistance box
III. Preparation for the Experiment (to be done together at the start of the lab session)
a) With Vs = 10V and Is = 1mA, analyze the circuit in Figure 2-1 and make a sketch of
the circuit with all node potentials and currents labeled on the sketch. You should define
the node potentials with respect to the reference node indicated. Verify by calculation
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that KCL is satisfied at each node and that KVL is satisfied around each mesh in the
circuit.
10k
a
b
2k
4.7k
Vs
Is
10k
Figure 2-1
b) According to the linearity and superposition theorems, you should be able to express
the voltage across terminals a-b as a linear combination of the independent sources, Vab
= αVs + βIs . Calculate the proportionality constants α and β for the given circuit.
c) Find the Thevenin equivalent circuit corresponding to terminals a-b in Fig. 2-1, if the
current source is removed.
d) What is the maximum power that can be drawn from terminals a-b in the circuit of
part (c), and what load resistance will draw this maximum power ?
IV. Experimental Procedure
a) On your protoboard, wire the circuit in Figure 2-2, leaving the two DC power
supplies, Vs and Vb, turned off for the time being. Measure each of the resistor values
with your multimeter before you place them on the board, and make a sketch of figure 22 to record the measured values (You will need to save this sketch for reference when
you write the report for this lab). In figure 2-2, the circuitry enclosed in the dashed
rectangle on the right will represent the ideal current source, Is in figure 2-1. You can
adjust the value of Is by adjusting the voltage Vb, and the 2kΩ resistor in the dashed box
will allow you to measure the current Is.
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10k
a
b
2k
4.7k
Is
2k
10k
V
s
V
I
V
b
Figure 2-2
Adjust the two DC power supplies so that Vs = 10V and Is = 1mA. The best procedure
is to use your digital multimeter to first adjust the Vs power supply to obtain Vs = 10V
and then adjust the Vb supply to obtain Is = 1mA . Next, using the multimeter, measure
the volt drop across each of the four resistors outside the dashed box, and record the
results on the sketch you have drawn, being sure to mark the proper polarities. Also
measure VI, and record its value on your sketch.
b) By adjusting the voltages of the two DC power supplies, you will now fill in the table
below. First, set Vs to 5V, then adjust the Vb supply so that Is takes the values 0.2mA,
0.5mA, and 1.0mA successively, to fill in the first column of the table. Each time you
adjust Is, measure the value of Vab and enter the number in the table box corresponding
to the settings of Vs and Is. Next, set Vs to 10V and repeat the three Is adjustments to fill
in the second column of the table. Finally, set Vs to15V, and complete the table.
I
Vs
s
5V
10V
0.2mA
0.5mA
1.0mA
10
15V
c) Remove from your circuit the power supply and the 2kΩ resistor contained in the
dashed box on the right side of figure 2-2, and connect a load resistance (your decade box
adjusted to maximum resistance) across terminals a-b (Remember to turn off all power
supplies before making any changes in the circuit). The circuit should now look like
figure 2-3.
10k
a
2k
b
4.7k
RL
10k
V
s
Figure 2-3
Reset the Vs power supply to 10V. Next, fill in the table below with 7 entry pairs by
setting the load resistance successively to the values RL = ∞, 10kΩ, 5kΩ, 2kΩ, 1kΩ, 500
Ω, 100Ω. For each new load setting measure the precise value of the load resistance and
the value of Vab using your digital multimeter, and record them in the table below.
RL
Vab
d) Now you will determine experimentally the load resistance that draws maximum
power when connected across terminals a-b in the circuit of figure 2-3. For any given
value of RL , the power delivered to RL is easily found by calculating PL = Vab2 / RL .
To determine the maximum power and the corresponding load resistance therefore, adjust
the decade box to its maximum setting and then reduce its resistance in steps, each time
measuring Vab and calculating PL from the formula given above. As you do this, do not
measure the value of RL each time, but use the value indicated on the decade box to
calculate PL. When you reach the value of RL that draws maximum power, record the
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value of PL and then measure the value of RL for this point only, making sure you
disconnect the decade box from the circuit before measuring its resistance. The value of
RL found here should be equal to the Thevenin resistance as seen from terminals a-b.
Now, in order to make an alternate measurement of the Thevenin resistance seen from
terminals a-b for the circuit of figure 2-3, remove the power supply and replace it with a
short circuit. Also check that the decade box is no longer connected, and then measure
the resistance across terminals a-b using your digital multimeter. Record the measured
value of Rth .
V. Report
a) We know that for the circuit in figure 2-1 we should have Vab = αVs + βIs .
Therefore, if we are given two pairs of source values (Vs1, Is1) and (Vs2, Is2) and the
corresponding output values Vab1 and Vab2 , we should be able to find the values of α
and β from the following pair of linear equations:
1
Vab
= αVs1 + βI1s
2
Vab
= αVs2 + βI2s
From the data you recorded in part (b) of the experiment, substitute the numbers from the
(Vs, Is) pairs (5V, 0.2mA) and (15V, 1.0mA) into the above equations and solve for α
and β. Then fill in the rest of the table below by using the formula Vab = αVs + βIs with
the values of α and β that you have just found.
Is
V
s
5V
10V
15V
0.2mA
0.5mA
1.0mA
Compare the numbers in this table to those you measured in part (b) of the experiment,
and explain any discrepancies you find.
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b) Copy the RL and Vab values from the table you filled in during part (c) of the
experiment into the table below, and then complete this table by using Ohm's law to find
the Iab values, where Iab is the current flowing from terminal a to terminal b through RL.
RL
Vab
I
ab
Next, plot Vab as a function of Iab on a sheet of graph paper. This is the v-i
characteristic for the circuit of figure 2-3 and should, in theory, look like the graph below.
V
ab
Voc
slope = - R
th
0
I sc
I ab
Estimate the slope of your graph and calculate Rth. How does this value compare with
the measured value of Rth that you found using the digital multimeter in part (c) of the
experiment ? How does it compare with the value of Rth you get when you short out the
voltage source in figure 2-3 and combine the resistors theoretically (As usual, use the
measured values for the resistors instead of those given in the figure) ? Also find the
open circuit voltage from your graph and draw the Thevenin equivalent circuit. Calculate
the maximum power that can be drawn from this circuit.
c) Compare values of Pmax and Rth that you measured in part (d) of the experiment to
those found in part (b) above. Once again, explain discrepancies.
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