Page 45 - Schaum's Outline of Theory and Problems of Electric Circuits

CIRCUIT LAWS
[CHAP. 3
34
Note: This is similar to the case of current division in a two-branch parallel circuit where the other resistor
0
has been replaced by R .
3.17 A power transmission line carries current from a 6000-V generator to three loads, A, B, and C. The loads
are located at 4, 7, and 10 km from the generator and draw 50, 20, and 100 A, respectively. The resistance of
the line is 0.1
/km; see Fig. 3-21. (a) Find the voltage at loads A, B, C. (b) Find the maximum percentage
voltage drop from the generator to a load.

Fig. 3-21

Ans.(a) v A ¼ 5928 V; v B ¼ 5889 V; v C ¼ 5859 V; (b) 2.35 percent

3.18 In the circuit of Fig. 3-22, R ¼ 0 and i 1 and i 2 are unknown. Find i and v AC .
Ans. i ¼ 4A; v AC ¼ 24 V

Fig. 3-22

3.19 In the circuit of Fig. 3-22, R ¼ 1
and i 1 ¼ 2 A. Find, i, i 2 , and v AC .
Ans. i ¼ 5A; i 2 ¼ 16 A; v AC ¼ 27 V

3.20 In the circuit of Fig. 3-23, i s1 ¼ v s2 ¼ 0, v s1 ¼ 9V, i s2 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 i BA and v AC .
Hint: A zero voltage source corresponds to a short-circuited element and a zero current source corresponds
to an open-circuited element.
8
> ðaÞ i BA ¼ 7; v AC ¼ 30
>
>
<
Ans: ðbÞ i BA ¼ 4:2; v AC ¼ 21:6 ðAll in A and V)
> ðcÞ i BA ¼ 3:5; v AC ¼ 19:5
>
>
:
ðdÞ i BA ¼ 0:006 0; v AC ¼ 9:02 9
3.21 In the circuit of Fig. 3-23, v s1 ¼ v s2 ¼ 0; i s1 ¼ 6A; i s2 ¼ 12 A: For the four cases of (a)
R ¼ 0; ðbÞ R ¼ 6
; ðcÞ R ¼ 9
; and ðdÞ R ¼ 10 000
; draw the simplified circuit and find i BA and v AC .
8
> ðaÞ i BA ¼ 6; v AC ¼ 36
>
>
<
Ans: ðbÞ i BA ¼ 3:6; v AC ¼ 28:8 ðAll in A and V)
> ðcÞ i BA ¼ 3; v AC ¼ 27
>
>
:
ðdÞ i BA ¼ 0:005 0; v AC 18