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Supplementary Problems
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3.9 Find the source voltage V and its polarity in the circuit shown in Fig. 3-15 if (a) I 2:0 A and (b) I 2:0 A. Ans. (a) 50 V, b positive; (b) 10 V, a positive. Find Req for the circuit of Fig. 3-16 for (a) Rx 1, Ans. (a) 36
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; (b) 16
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; (c) 20
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(b) Rx 0, (c) Rx 5
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CHAP. 3]
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CIRCUIT LAWS
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Fig. 3-16 Fig. 3-15 3.11 An inductance of 8.0 mH is in series with two inductances in parallel, one of 3.0 mH and the other 6.0 mH. Find Leq . Ans. 10.0 mH Show that for the three capacitances of equal value shown in Fig. 3-17 Ceq 1:5 C:
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Fig. 3-17 Fig. 3-18
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Find RH and RO for the voltage divider in Fig. 3-18 so that the current I is limited to 0.5 A when VO 100 V. Ans: RH 2 M
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; RO 200
Using voltage division, calculate V1 and V2 in the network shown in Fig. 3-19.
Ans.
11.4 V, 73.1 V
Fig. 3-20 Fig. 3-19
Obtain the source current I and the total power delivered to the circuit in Fig. 3-20. Ans. 6.0 A, 228 W
Show that for four resistors in parallel the current in one branch, for example the branch of R4 , is related to the total current by   R0 R1 R2 R3 where R 0 I4 IT R4 R 0 R1 R2 R1 R3 R2 R3
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Note: This is similar to the case of current division in a two-branch parallel circuit where the other resistor has been replaced by R 0 . 3.17 A power transmission line carries current from a 6000-V generator to three loads, A, B, and C. The loads are located at 4, 7, and 10 km from the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 5928 V; vB 5889 V; vC 5859 V; 3.18
(b) 2.35 percent
In the circuit of Fig. 3-22, R 0 and i1 and i2 are unknown. Find i and vAC . Ans. i 4 A; vAC 24 V
Fig. 3-22
In the circuit of Fig. 3-22, R 1
and i1 2 A. Ans. i 5 A; i2 16 A; vAC 27 V
Find, i, i2 , and vAC .
In the circuit of Fig. 3-23, is1 vs2 0, vs1 9 V, is2 12 A. For the four cases of (a) R 0, (b) R 6
, (c) R 9
, and (d) R 10 000
, draw the simpli ed circuit and nd 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 > a iBA 7; vAC 30 > > < b i 4:2; v 21:6 BA AC Ans: All in A and V) > c iBA 3:5; vAC 19:5 > > : d iBA 0:006 % 0; vAC 9:02 % 9 In the circuit of Fig. 3-23, vs1 vs2 0; is1 6 A; is2 12 A: For the four cases of (a) R 0; b R 6
; c R 9
; and d R 10 000
; draw the simpli ed circuit and nd iBA and vAC . 8 > a iBA 6; vAC 36 > > < b i 3:6; v 28:8 BA AC Ans: All in A and V) > c iBA 3; vAC 27 > > : d iBA 0:005 % 0; vAC % 18
CHAP. 3]
CIRCUIT LAWS
Fig. 3-23
In the circuit Fig. 3-23, vs1 0, vs2 6 V, is1 6 A, is2 12 A. For the four cases of (a) R 0, (b) R 6
, (c) R 9
, and (d) R 10 000
, draw the simpli ed circuit and nd iBA and vAC . 8 > a > > < b > c > > : d iBA iBA iBA iBA 5:33; vAC 34 3:2; vAC 27:6 2:66; vAC 26 0:005 % 0; vAC 18:01 % 18
Ans:
(All in A and V)
In the circuit of Fig. 3-24, (a) nd the resistance seen by the voltage source, Rin v=i, as a function of a, and (b) evaluate Rin for a 0; 1; 2. Ans. (a) Rin R= 1 a ; (b) R; 1; R
Fig. 3-24
In the circuit of Fig. 3-24, (a) nd power P delivered by the voltage source as a function of a, and (b) evaluate P for a 0; 1; 2. Ans. (a) P v2 1 a =R; (b) v2 =R; 0; v2 =R In the circuit of Fig. 3-24, let a 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 0:99R, (b) P v2 = 99R
Fig. 3-25
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