ELEC 1104

11.

University of Hong KongDepartment of Electrical & Electronic Engineering

Problem SheetPower in A.c. Circuits

A single-phase load consisting of an impedance of 30+j 10 ohms is connected to a200 V supply. Determine the load current, load power and power factor. If thesupply voltage is upgraded to 230 V, what is the percentage change in the loadcurrent and load power consumed?

(Ans: 6.325A; 1200W; 0.95 lagging; 15%; 32%)~ Q

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=- [1..00 W 1/A single-phase motor draws a current of 10 A from a 220 V, 50 Hz supply. If themotor delivers a load of 1.5 kW and the motor efficiency is 85%, calculate:

(a) The active, reactive and apparent power supplied to the motor;(b) The power factor of the motor load.

(Ans: 1.765kW; 1.313kVAr; 2.2 kVA; 0.8 lagging)

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A single-phase line supplies simultaneously the following llads:(a) 2 kW at unity power factor;(b) 3 kVA at 0.75 power factor lagging;(c) 1.95 kWat 0.95 power factor leading.

Calculate the total active, reactive and apparent power supplied by the source andthe power factor.

2/.

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(Ans: 6.2kW; 1.343kV Ar; 6.344kVA; O.977Iagging)

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ELEC 1104

4/. A 6.6 kV, 50 Hz, three-phase star-connected generator supplies a balanced three-phase load of 4,000 kW at a p.f. of 0.8 lagging. Calculate the line current.If the load p.f. is raised to 0.95 with the line current remaining the same, what willbe the new output power to the load?

(Ans: 437.4A; 4750 kW)

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5/. A 3.3 kjV, 50 Hz three-phase line is supplying power to a lagging power factor0,,'1 load. Tfo wattmeters are used to measure the power consumed. If one wattmeter

I_or>- I" reads 198 kW and the other reads 396 kW, determine the line current, the active,., ,)1\/ IY\ x,JY and apparent power of the load and the load power factor.

'-.Y (Ans: 120A; 594 kW; 686 kVA; 0.866 lagging)

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Thr: i~ent~cal coils, each having a resistance of20 ohms and a reactance of 15ohms, 'E.e connected in star to a 400 V, three-phase, 50 Hz supply. Calculate:

(a) Ilhe line current;(b) [The power supplied;(c) [The power factor.

Iftwo tattmeters are used to measure the total power and their current coils areconnected to phase 'A' and phase 'B' respectively, how should their voltage coilsbe connected? What are the wattmeter readings? Assume phase sequence A-B-C.(,t~C J b-C

I (Ans: 9.24A; 5.12kW; 0.8 lagging; 3.67kW;1.45kW)

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6/.

ELECI104

7/. If in Q~three identical capacitors are connected in delta to the same supply suchthat they are in parallel with the load, calculate

(a) The capacitance required to give a resultant power factor of 0.95 lagging;(b) The line current taken by the combined circuit.

Assume capacitors are lossless.(Ans: 14.3 uF; 7.78A)

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V - ~ 11-f~ "- qP ~ G~ I (Ans: 27.7A; 15.36kW; 0.8; 11.00kW; 4.36kW) ::::. ?:<''Z ..>rJ _ 2..-0-£- J- l )' ?\~ . ~ ~ l+ '0.. ~C) C~~ \~(t~ --) 3 :: o. % '/ . C WXC(6

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9/. Non-reactive loads of 10,6 and 4 kW are connected between the neutral and the'R', 'Y' and 'B' phases respectively of a 400 V, three-phase, 4-wire system. Find =- 7,I~,f;/

the current in each line conductor and the neutral. Assume phase sequence R-Y-B. r;(Ans: 43.3A; 26.0A; 17.3A; 22.9A)

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ELEC 1104

10/ Repeat Q9 if the constant impedance loads are connected across phases R-Y,Y-B and B-R respectively of a 400 V, three-phase 3-wire system.

(Ans: 162.3A; 181.9A; 113.3A)

111. A star-connected load comprising two resistors and a pure inductor of the samenumerical impedance are connected to a symmetrical three-phase supply. Find thevoltage across each branch as a percentage of the line voltage.

~f ~' t~r:u-~ ~ r(Ans: 23.2%; 86.4%; 77.5%)

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A 3461200 V, 50 Hz, 3-phase, 4-wire supply is delivering power to a 10 kVA, ;)three-phase induction motor at a power factor of 0.75 lagging. There is also a 1.5kW single-phase unity power factor load connected to phase 'A'. Calculate thephase 'A' line current.

12/.

If a wattmeter has its current coil connected in the phase 'A' conductor and itsvoltage coil connected across the phase 'B' and phase 'C' conductors, determinethe wattmeter reading.

(Ans: 22.84A; 3820 W)2.

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