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EXPERIMENT 1

THEVENIN'S THEOREM

OBJECTIVE

To gain familiarity with the test equipment and to demonstrate the usefulness of

Thevenin's theorem.

THEORY

Thevenin's theorem states that any point in a linear circuit can be represented by a resistor

in series with a voltage source to ground (Fig. 1). The value of the resistance does not depend on

the value of the voltage source, and vice versa. For example, the value of the resistance is

unchanged if the voltage source is reduced to zero volts. More generally, any point in a linear dc

circuit can be characterized by measuring the voltage at that point (say, with a voltmeter) and the

resistance at that point. The resistance is the value that would be measured with an ohmmeter

from that point to ground if all the supply voltages were set to zero volts. Note that the internal

resistance of an ideal voltage supply is zero ohms, whatever its voltage.

RESISTANCE TO GROUND

Use the digital ohmmeter to measure the resistance to ground of all the circuits in Fig. 2.

Your answers for 2a, 2b, and 2c should be the same as the value of the resistor, since in each

case one end of the resistor is connected to ground.

In Figs. 2d, 2e, and 2f, the resistors are in "series." In this case the total resistance is

given by

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R R R= + −1 2 1 1 ( )

Note that if one resistor is much larger than the other, as in Fig. 2f, R for practical purposes

pretty much equals the larger resistor.

In Figs. 2g, 2h, and 2i, the resistors are in "parallel." In this case the total resistance is

given by

RR R

R R=

+−1 2

1 2

1 2 ( )

Note that if one resistor is much larger than the other, as in Fig. 2i, R for practical purposes

pretty much equals the smaller resistor.

Use the digital ohmmeter to measure the resistance to ground at the terminals of the

circuits in Fig. 3. In these circuits, both ends of the resistance are connected to ground.

Obviously, the resistance to ground at the ends is (nominally) zero, since those points are directly

connected to ground.

Note that Fig. 3a is the same as Fig. 2g, and that tap number 2 of Fig. 3b is similar to the

output of Fig. 2h. Suppose you had a circuit like that in Fig. 3b, but with ten 1 kΩ resistors in

series, instead of only four. What would be the resistance to ground at the central tap? What

would be the resistance to ground at tap number 2?

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VOLTAGE TO GROUND

Measure the voltage to ground at the terminals in Fig. 4a. The voltages at terminals 1 and

3 are obvious; the voltage at terminal 2 may be computed by first using Ohm's law to find the

current in the circuit,

I V R= −/ ( )1 3

where V = 12 Volts and R = 2 kΩ. This gives a value for the current of (nominally) 6 mA. The

voltage across the bottom resistor is then computed, using Ohm's law again, but with R = 1 kΩ.

This gives a voltage at terminal 2 of (nominally) 6 Volts. Alternatively, there's an obvious

symmetry - there must be the same voltage across each of the resistors, because they are equal,

so therefore the voltage at terminal 2 is half the supply voltage, or (nominally) 6 Volts.

Measure the voltage to ground at the terminals in Fig. 4b. Because the resistors are all

equal the voltages should be equally spaced.

Measure the voltage to ground at terminal 2 in Fig. 4c. How does this circuit compare to

the circuit in Fig. 4b? What point in Fig. 4b corresponds to terminal 2 in Fig. 4c?

ASSIGNMENT

Use the measurements you made on the circuits in Figs. 3 and 4 to compute the Thevenin

equivalent resistors and voltages for each of the terminals in Figs. 4a, 4b, and 4c. What

assumption is implicit regarding the internal impedance of the voltage source?

Assume that terminal 2 in Figs. 4a, 4b, and 4c is connected directly to ground by zero

resistance. Use Fig. 4 and Ohm’s law (equation 1-3) to find what currents would flow to ground.

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Repeat, using the Thevenin equivalents to terminal 2 you computed above. How do your answers

compare?

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1kΩ1kΩ

1kΩ

1kΩ 1kΩ 1kΩ2kΩ

3kΩ 10kΩ

2a 2b 2c2d 2e 2f

1kΩ 1kΩ 1kΩ 3kΩ 1kΩ

2g 2h 2i

Fig 2

1kΩ

1kΩ

1

2

3

1kΩ

1kΩ

1kΩ

1kΩ

1

2

3

4

53a

3b

1kΩ

1kΩ

1

2

3

1

2

3

4

5

1kΩ

1kΩ

1kΩ

1kΩ

4b

12 volt s

4a

12 volt s

1kΩ

3kΩ

1

2

3

4c

Figures

V

R

Fig 1

Fig 3

Fig 4

10kΩ

12 volt s