CHAP. 3]

CIRCUIT LAWS

35

Fig. 3-23

3.22

In the circuit Fig. 3-23, vs1 ¼ 0, vs2 ¼ 6 V, is1 ¼ 6 A, is2 ¼ 12 A. For the four cases of (a) R ¼ 0, (b) R ¼ 6 , (c) R ¼ 9 , and (d) R ¼ 10 000 , draw the simpliﬁed circuit and ﬁnd iBA and vAC .

Ans:

3.23

8 ðaÞ > > > < ðbÞ > ðcÞ > > : ðdÞ

iBA iBA iBA iBA

¼ 5:33; vAC ¼ 34 ¼ 3:2; vAC ¼ 27:6 ¼ 2:66; vAC ¼ 26 ¼ 0:005  0; vAC ¼ 18:01  18

(All in A and V)

In the circuit of Fig. 3-24, (a) ﬁnd the resistance seen by the voltage source, Rin ¼ v=i, as a function of a, and (b) evaluate Rin for a ¼ 0; 1; 2. Ans. (a) Rin ¼ R=ð1  aÞ; (b) R; 1; R

Fig. 3-24

3.24

In the circuit of Fig. 3-24, (a) ﬁnd power P delivered by the voltage source as a function of a, and (b) evaluate P for a ¼ 0; 1; 2. Ans. (a) P ¼ v2 ð1  aÞ=R; (b) v2 =R; 0; v2 =R

3.25

In the circuit of Fig. 3-24, let a ¼ 2. Connect a resistor Rx in parallel with the voltage source and adjust it within the range 0  Rx  0:99R such that the voltage source delivers minimum power. Find (a) the value of Rx and (b) the power delivered by the voltage source. Ans. (a) Rx ¼ 0:99R, (b) P ¼ v2 =ð99RÞ

Fig. 3-25

Mahmood_Nahvi_eBook_Schaum_s_Outlines_Theory_An
Mahmood_Nahvi_eBook_Schaum_s_Outlines_Theory_An