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34

CIRCUIT LAWS

[CHAP. 3

Note: This is similar to the case of current division in a two-branch parallel circuit where the other resistor has been replaced by R 0 . 3.17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) vA ¼ 5928 V; vB ¼ 5889 V; vC ¼ 5859 V; 3.18

(b) 2.35 percent

In the circuit of Fig. 3-22, R ¼ 0 and i1 and i2 are unknown. Find i and vAC . Ans. i ¼ 4 A; vAC ¼ 24 V

Fig. 3-22

3.19

In the circuit of Fig. 3-22, R ¼ 1 and i1 ¼ 2 A. Ans. i ¼ 5 A; i2 ¼ 16 A; vAC ¼ 27 V

Find, i, i2 , and vAC .

3.20

In the circuit of Fig. 3-23, is1 ¼ vs2 ¼ 0, vs1 ¼ 9 V, 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 . Hint: A zero voltage source corresponds to a short-circuited element and a zero current source corresponds to an open-circuited element. 8 ðaÞ iBA ¼ 7; vAC ¼ 30 > > > < ðbÞ i ¼ 4:2; v ¼ 21:6 BA AC Ans: ðAll in A and V) > ¼ 3:5; v ðcÞ i > BA AC ¼ 19:5 > : ðdÞ iBA ¼ 0:006  0; vAC ¼ 9:02  9

3.21

In the circuit of Fig. 3-23, vs1 ¼ vs2 ¼ 0; is1 ¼ 6 A; is2 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 iBA and vAC . 8 ðaÞ iBA ¼ 6; vAC ¼ 36 > > > < ðbÞ iBA ¼ 3:6; vAC ¼ 28:8 Ans: ðAll in A and V) > > > ðcÞ iBA ¼ 3; vAC ¼ 27 : ðdÞ iBA ¼ 0:005  0; vAC  18

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