36

CIRCUIT LAWS

[CHAP. 3

3.26

In the circuit of Fig. 3-25, R1 ¼ 0 and b ¼ 100. 10 k . Ans. v ¼ 1; 10 V

Draw the simpliﬁed circuit and ﬁnd v for R ¼ 1 k and

3.27

In the circuit of Fig. 3-25, R1 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; 2 V

3.28

In the circuit of Fig. 3-25, R1 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 i¼ 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

Mahmood_Nahvi_eBook_Schaum_s_Outlines_Theory_An
Mahmood_Nahvi_eBook_Schaum_s_Outlines_Theory_An