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