Page 47 - Schaum's Outline of Theory and Problems of Electric Circuits

P. 47

CIRCUIT LAWS
[CHAP. 3
36
3.26 In the circuit of Fig. 3-25, R 1 ¼ 0 and b ¼ 100. Draw the simpliﬁed circuit and ﬁnd v for R ¼ 1 k
and
10 k
. Ans. v ¼ 1; 10 V

3.27 In the circuit of Fig. 3-25, R 1 ¼ 0 and R ¼ 1 k
. Draw the simpliﬁed circuit and ﬁnd v for b ¼ 50; 100; 200.
Note that v changes proportionally with b. Ans. v ¼ 0:5; 1; 2V

3.28 In the circuit of Fig. 3-25, R 1 ¼ 100
and R ¼ 11 k
. Draw the simpliﬁed circuit and ﬁnd v for
b ¼ 50; 100; 200. Compare with corresponding values obtained in Problem 3.27 and note that in the present
case v is less sensitive to variations in b. Ans. v ¼ 0:90; 1; 1:04 V

3.29 A nonlinear element is modeled by the following terminal characteristic.

10v when v 0
i ¼
0:1v when v 0
Find the element’s current if it is connected to a voltage source with (a) v ¼ 1 þ sin t and (b) v ¼ 1 þ sin t.
See Fig. 3-26(a). Ans. (a) i ¼ 10ð1 þ sin tÞ; (b) i ¼ 0:1ð 1 þ sin tÞ

Fig. 3-26

3.30 Place a 1-
linear resistor between the nonlinear element of Problem 3.29 and the voltage source. See Fig.
3-26(b). Find the element’s current if the voltage source is (a) v ¼ 1 þ sin t and (b) v ¼ 1 þ sin t.
Ans.(a) i ¼ 0:91ð1 þ sin tÞ; (b) i ¼ 0:091ð 1 þ sin tÞ

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