Basic Circuit Theory With reference to the circuit shown in Fig. 11-22, let Van=12 Z0 kV and assume"+""phase sequence. The balanced source supplies IMW and 0.2M VAR. If R=12Q2, find:(a)the line current; (b)Zp; (c)the transmission efficiency R DOcos 500r V b Fig. 11-22 For prob. I Fig. 11-23 For prob. 2 2 Find the reading of the wattmeter in Fig. 11-23 3 A balanced three-phase system has a A-connected load with 10+j4@2 in each phase and is supplied by a source with v=250V.(a) Find the line current and the total power drawn by the load. (b) To what minimum value can the line current be reduced by installine equal capac reactances across each phase?(c)What size capacitors should be used at 60 Hz?(d) With the capacitors in phase what is the total power delivered to the load 4 a balanced 230V three-phase source is furnishing 6kVa at 0.83 Pf lagging to two A-connected parallel loads. One is a purely resistive load drawing 2kw. Determine the phase impedance of the second load 5 A 230V(line voltage) balanced three-phase system contains a A-connected load having 12+j3Q2 per phase and also a Y-connected load with 5+j1@2 per phase. Find the line current, the power taken by the combined load, and the load PF. 6 Three ideal wattmeters are arranged as shown in Fig. 11-24. Let v 4B=125 20 V and assume +"phase sequence. Each phase contains a 24Q2 resistor in series with a capacitive reactance of 7 Q2 where the three capacitors have a common node at N. Let point x be located between the resistor and capacitor in phase A, and find each wattmeter reading 7 Two wattmeters are used as shown in Fig. 11-25 to measure power. Determine the total power B B Z,|/g b。*(w b。 01z。|∠ Fig.11-25F Fig 11-24 For bAlIan Maritime University
Basic Circuit Theory Chpter11Problems 1 With reference to the circuit shown in Fig. 11-22, let =12 kV and assume “ + ” phase sequence. The balanced source supplies 1MW and 0.2M VAR. If R =12 V an • o ∠0 w Ω , find: (a) the line current; (b) Z ; (c) the transmission efficiency. P DaLian Maritime University 1 c V b 2 Find the reading of the wattmeter in Fig. 11-23 3 A balanced three-phase system has a ∆ −connected load with 10+j4Ω in each phase and is supplied by a source with V =250V. (a) Find the line current and the total power drawn by the load. (b) To what minimum value can the line current be reduced by installine equal capacitive reactances across each phase? (c) What size capacitors should be used at 60 Hz? (d) With the capacitors in phase what is the total power delivered to the load? L 4 A balanced 230V three-phase source is furnishing 6kVA at 0.83 PF lagging to two connected parallel loads. One is a purely resistive load drawing 2kW. Determine the phase impedance of the second load. ∆ − 5 A 230V (line voltage) balanced three-phase system contains a ∆ −connected load having 12+j3Ω per phase and also a Y- connected load with 5+j1Ω per phase. Find the line current, the power taken by the combined load, and the load PF. 6 Three ideal wattmeters are arranged as shown in Fig. 11-24. Let =125 V and assume “ + ” phase sequence. Each phase contains a 24 V AB • o ∠0 Ω resistor in series with a capacitive reactance of 7Ω where the three capacitors have a common node at N. Let point x be located between the resistor and capacitor in phase A, and find each wattmeter reading. 7 Two wattmeters are used as shown in Fig. 11-25 to measure power. Determine the total power, - + Fig. 11-22 For prob.1. C a N A B n V a n • b n • V c n • R w R w R w Z p Z p Z p + − + − Fig. 11-23 For prob.2. + - + - C i 100µF A 20 2.5sin500t 100µF C i 200cos500tV * * * * * * * * C A B W W WA B C b a c x N * * * * W 2 C A B W 1 b a c | Z p | /ϕ | Z p | /ϕ | Z p | /ϕ Fig. 11-25 For prob.7. Fig. 11-24 For prob.6
Basic Circuit Theory the PF, and the impedance in each phase of the A- connected load if the line voltage is 120V and (a)P1=-500W,P2=1300W;(b)P1=1300W,P2=500W 8 Fig. 1 1-26 shows a balanced three-phase three-wire system with positive phase sequence. Let V BC=120 260V andR =0.6Q2. If the total load(including wire resistance)draws 5k Va at PF=0. 8 lagging. Find(a) the total power lost in the resistance, and(b)v R R Fig. 11-26 For prob. 8 9 Fig. 11-27 shows a balanced three-phase three-wire circuit Letr =0 and v an=200 V Each phase of the load absorbs a complex power, Sp=2-jl kVA( i.e. Pp= 2kW, Qp=lk R R Fig. 11-27 For prob. 9 10 In the balanced three-phase system of Fig 11-26, let Z p=12+j5Q2 and 1 bB=20 A with phase sequence. If the source is operating with a power factor of 0.935, find(a)R, v and V AB; (b) the complex power supplied by the source DaLian Maritime University
Basic Circuit Theory Chpter11Problems the PF, and the impedance in each phase of the ∆ - connected load if the line voltage is 120V and (a) P1= - 500W, P =1300W; (b) P1=1300W, P =- 500W. 2 2 8 Fig. 11-26 shows a balanced three-phase three-wire system with positive phase sequence. Let =120 V and R = 0.6 . If the total load (including wire resistance) draws 5k VA at PF=0.8 lagging. Find (a) the total power lost in the resistance, and (b) . V BC • o ∠60 w Ω V an • - + C a b N c A B n V a n • V b n • V c n • R w R w R w Z p Z p Z p + − + − Fig. 11-26 For prob.8. 9 Fig. 11-27 shows a balanced three-phase three-wire circuit. Let R = 0 and =200 V. Each phase of the load absorbs a complex power, = 2 – j1 kVA ( i.e. P = 2kW, Q =- 1k VAR). If positive phase sequence is assumed, find , Z , and . w V an • o ∠60 − S P P P V bc • P I aA • - + Z C a b c A + B n V a n • V b n • V c n • R w R w R w p Z p Z p + − − Fig. 11-27 For prob.9. 10 In the balanced three-phase system of Fig. 11-26, let Z = 12+j5 P Ω and = 20 A with “ + ” phase sequence. If the source is operating with a power factor of 0.935, find (a) R , , and ; (b) the complex power supplied by the source. I bB • o ∠0 w V bn • V AB • DaLian Maritime University 2
Basic Circuit Theory ChpterlI Probler Reference answers to Selected Problems l:(a)283A;(b)412∠l1.64g;(c)97.1% 2:1876W. 3:(a)40.2A,16.16kW;(b)37.3A;,(c)21.9F,(d)16.16kW 4:354∠48.3°g 5:582A,22.6kW,0.975lag 6:PA=200W,PB=149.5W,Pc=250.5W 7:(a)800W,0.249lag,13.42∠756°9;(b)800W,0.249lag,1342∠-756°9 8:(a)1.042kW,(b)81.29∠1439V 9:(a)3464∠-30°V,(b)48-j24_;(c)1l18∠8657°A 10:(a)1.182g;(b)282∠20.77°V,(c)450.3∠1726V,(d)15826kVA DaLian Maritime University
Basic Circuit Theory Chpter11Problems Reference Answers to Selected Problems DaLian Maritime University 1: (a) 28.3A; (b) 412 Ω ; (c) 97.1%. o ∠11.64 2: 187.6W. 3: (a) 40.2A, 16.16 kW; (b) 37.3A; (c) 21.9 µ F; (d) 16.16 kW. 4: 35.4 . o ∠ Ω 48.3 5: 58.2A, 22.6 kW, 0.975 lag. 6: P =200W, P =149.5W, P C =250.5W. A B 7: (a) 800W, 0.249 lag, 13.42 o ∠75.6 Ω ; (b) 800W, 0.249 lag., 13.42∠ Ω . o − 75.6 8: (a) 1.042 kW; (b) 81.29 V. o ∠143.9 9: (a) 346.4 V; (b) 48-j24 ; (c) 11.18 A. o ∠ − 30 Ω o ∠86.57 10: (a) 1.182Ω ; (b) 282 V; (c) 450.3 V; (d) 15.82-j6 kVA. o ∠20.77 o ∠172.6 3