Exp 1 Thevenin,s[1]

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 = R1 + R2

(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

R=

R1 R2 R1 + R2

(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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Figures R 1 kΩ

V 2a

2b

1kΩ

1 kΩ

1 kΩ

1kΩ

3 kΩ

1 0kΩ

2 kΩ

1 kΩ

2c 2d

2e

2f

Fig 1 1 kΩ

1kΩ

1kΩ

3 kΩ

1kΩ

1 0kΩ

1 1 kΩ 2g 1 kΩ

2h

2i

2

1 1 kΩ 2 1 kΩ

Fig 2

3 1 kΩ

3

1 2 volt s

4 1 kΩ 3a

1 5

1k Ω

1 2 volt s

1 2 volt s 2

3b

1

Fig 3

1

1 kΩ

1 kΩ

1 kΩ 3 2

2

1 kΩ

1 kΩ

3 kΩ

4 3

1 kΩ

4a

5

4b

Fig 4

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3

4c