Basic Circuit Theory Chpter10 Problems I The physical construction of three pairs of coupled coils is shown in Fig. 10-16. Show two different possible locations for the two dots on each pair of coils 2 For the circuit illustrated in Fig. 10-17(a) find I and VR:(b) repeat if a 6Q2 resistor is connected between the terminals at the right 6 For pr 4H k=0.71x F-3H 5H (20H 8H C18H @=5rad/s Fig. 10-17 For prob. 2 Fig. 10-18 For prob. 3 3 Let 1,=5 sin 40t A and 12=2 sin 40t A in Fig. 10-18. Find i,(t)and v(t). Is the direction of average power flow to the right or to the left in the center of the circuit? 4 If the circuit shown in Fig. 10-19 is series resonant at @.=lk rad/s find C and Q k=0.5 IHD C4H 25mH Fig. 10-19 For prob. 4 Fig 10-20 For prob.5 5 In Fig. 10-20, let Z, be a 4 u F capacitor having an-j25Q2 and calculate Z in when k=(a)0; (b)0.5;(c)1 6 Find the average power delivered to each resistor in the circuit shown in Fig. 10-21 129 00V 5Q 2Q Fig. 10-21 For prob. 6 Fig. 10-22 For prob. 7 DaLian Maritime University
Basic Circuit Theory Chpter10 Problems 1 The physical construction of three pairs of coupled coils is shown in Fig. 10-16 . Show two different possible locations for the two dots on each pair of coils. 2 For the circuit illustrated in Fig. 10-17 (a) find and ; (b) repeat if a 6Ω resistor is connected between the terminals at the right. • A I • V B 1 2 4 3 1 4 2 3 1 4 2 3 (a) (b) (c) Fig. 10-16 For prob.1. - + - + 10Ω 100 4H ω = 5rad / s / 0°V 3H 5H I A • V B • - + x i 1 i 2 i v k = 1 5H k = 0.7 20H 8 H H 18 Fig. 10-17 For prob.2. Fig. 10-18 For prob.3. 3 Let i 1= 5 sin 40t A and i = 2 sin 40t A in Fig. 10-18. Find i (t) and v(t). Is the direction of average power flow to the right or to the left in the center of the circuit? 2 x 4 If the circuit shown in Fig. 10-19 is series resonant at ω r = 1k rad/s find C and Q. + - C V s 4H 10Ω • 1H 10Ω k = 0.5 20Ω 2Ω in 25mH Z Z L k 100mH Fig. 10-19 For prob.4. Fig. 10-20 For prob.5. 5 In Fig. 10-20, let Z be a 4 L µ F capacitor having an – j25Ω and calculate Z in when k = (a) 0; (b) 0.5; (c) 1. 6 Find the average power delivered to each resistor in the circuit shown in Fig. 10-21. - - + - + + 1 • V 2 • V / 0°V x 120 1 : a 12 Ω 36 Ω 5 : 1 y + - 2Ω 5Ω 3 Ω 30/ 0°V 1 : 2 Fig. 10-21 For prob.6. Fig. 10-22 For prob.7. DaLian Maritime University 1
Basic Circuit Theory Chpter10 Problems 7(a) In the circuit of Fig. 10-22 find the turns ratio a and the average power delivered to each resistor.(b)If there is no voltage between points x and y, determine V, and v2 8 It is desired to connect a resistor between points a and b in Fig. 10-23. (a)What is the maximum power that can be delivered to this resistor and what should the value of resistance be?(b) Repeat for the where the dot is at the lower terminal of the secondary winding 90ga10910:119 1000° 2kQ 00°V 3Ω √2 0=NoRad/s Fig. 10-23 For prob. 8 Fig. 10-24 For prob. 9and 10 9 In the circuit shown in Fig. 10-24, find the average power absorbed by (a) the source; (b)each of the two resistors; (c)each of the two inductances; (d) the mutual inductance 10(a) Find the Thevenin equivalent network faced by the 2 k Q2 resistor in the circuit of Fig. 10-24 (b)What is the maximum average power that can be drawn from the network by an optimum value of z,(instead of kQ2)? Reference answers to Selected Problems l:(a)l-3or2-4;(b)2-3orl-4,(c)2-3or1-4 2:(a)3.7142A,374∠218°V(b4.296∠-589°A,159∠-17.1V 3: 2.11 sin 40t A.-286 cos 40t 4:1.333FF,462. 5:20+j10009,20+722.292,20j119 6:P3=119.7W,P2=199W,Ps=499W 7:(a)a=1,p12108W,P36=324W,(b)V1=V2=108∠180°V 8:(a)6429,562W,(b)85892,564W 9:(a)-10.4W;(b)Ps0=563,P20004.7w,(c) 0 each;(d)0 0:(a)oc=145.5∠-1666°V,Zm=1059+76.592;(b)25W DaLian Maritime University
Basic Circuit Theory Chpter10 Problems 7 (a) In the circuit of Fig. 10-22 find the turns ratio α and the average power delivered to each resistor. (b) If there is no voltage between points x and y, determine and . • V1 • V2 8 It is desired to connect a resistor between points a and b in Fig. 10-23. (a) What is the maximum power that can be delivered to this resistor and what should the value of resistance be? (b) Repeat for the where the dot is at the lower terminal of the secondary winding. + - 50Ω 3H ω 2 100 / 0°V = 100rad/s 2kΩ + 2 H 5 H - 90 Ω a 10Ω 50 / 0°V 3 Ω 10 : 1 1Ω b Fig. 10-24 For prob.9and 10. Fig. 10-23 For prob.8. 9 In the circuit shown in Fig. 10-24, find the average power absorbed by (a) the source; (b) each of the two resistors; (c) each of the two inductances; (d) the mutual inductance. 10 (a) Find the Thevenin equivalent network faced by the 2 kΩ resistor in the circuit of Fig. 10-24. (b) What is the maximum average power that can be drawn from the network by an optimum value of Z (instead of 2 k )? L Ω Reference Answers to Selected Problems 1: (a) 1—3 or 2—4; (b) 2—3 or 1—4, (c) 2—3 or 1—4. 2: (a) 3.714 A, 37.14 V;(b)4.296 A, 15.96 V. 2 o ∠21.8 o ∠ − 58.9 o ∠ −17.1 3: 2.11 sin 40t A, -286 cos 40t. 4: 1.333F µ F, 46.2. 5: 20+j1000Ω , 20+j722.2Ω , 20-j111Ω . 6: P =119.7W, P 2 =19.9W, P =49.9W, 3 5 7: (a) α =1, p12 108W, P =324W; (b) V1=V =108 V. 36 2 o ∠180 8: (a) 64.2Ω , 5.62W; (b) 85.8Ω , 56.4W. 9: (a) –10.4W; (b) P =5.63, P =4.77W; (c) 0 each; (d) 0. 50 2000 10: (a) =145.5 V, Z =105.9+j76.5 • V OC o ∠ −166.6 th Ω ; (b) 25W. DaLian Maritime University 2
