ESO-210: Introduction to Electrical Engineering

(2014-2015, First Semester)

Tutorial Assignment No. # 4

1. Considering given fig, let balanced positive sequence, 3-ϕ voltages with VAB = 0100 3 0 V (rms) be applied to terminals A, B, and C. The 3-ϕ star-connected balanced

load consists of a per-phase impedence of (10+j10) ohm. Determine the wattmeter

readings of a WA and WC. Then find the total 3-ϕ real and reactive powers delivered to

the load. Based on the wattmeter readings of WA and WC, compute the load power factor

and check the sign associated with the power factor angle.

Q1 Ans: WA =317 W and WC =1183W , PF angle = 45 deg (lagging)

2. While performing a load test on a 3-ϕ wound-rotor induction motor by two wattmeter’s

method, the readings obtained on two wattmeters were +14.2kW and -6.1kW and the line

voltage is 440V. Calculate:

a) True power drawn by motor

b) Power factor, and

c) Line current Q2 Ans: a) 8.1 kW b) 0.2249 lag c) 47.26 A

3. Two wattmeters have been used to measure the power input to a 150 kW, 440 V, 3-ϕ slip

ring induction motor running at full load. The wattmeter readings are 115 kW and 50 kW.

Calculate (i) the input to the motor, (ii) power factor of the motor, (iii) line current drawn by

the motor, and iv)efficiency of motor Q3 Ans: i) 165 kW ii) 0.826 iii) 262.1A iv) 90.9%

4. A balanced star-connected load is supplied from a symmetrical, 3-ϕ, 440 V, 50 Hz supply

system. The current in each phase is 20 A and lags behind its phase voltage by an angle 40°.

Calculate (i) phase voltage, (ii) load parameters, (iii) total power and (iv) readings of two

wattmeters, connected in the load circuit to measure the total power.

Q4 Ans: i) 254 V ii) Zph=12.7 R = 9.73 , X=8.163 iii) 11.6745kW, iv) W1=8.665kW,

W2=3.009kW

5. Find the line currents and real power absorbed by the load in the unbalanced 3-ϕ circuit as

shown in figure.

0120 120120

240120

)10(

)10( j

)5( jA

CB

a

bc

aI

bI

cI

Q5 Ans:Line currents Ia = 064 80.1 A, Ib = 038.1 60 A, Ic = 042.5 225 A, Power=4.84kW

6. For the unbalanced circuit shown in Fig., find (a) the line currents, (b) the total complex

power absorbed by the load, and (c) the total complex power supplied by the source.

0220

120220 240220

)5(

)5( j

)5.2( j

A

CB

a

bc

nN

aI

bI

cI

Q6 Ans:a) Ia = 0208.18 0 A, Ib = 0156.76 24.90 A, Ic = 093.33 134.99 A, b) (0.43558-

j0.1452)*1e5 VA, c) (-0.43558+j0.1452)*1e5 VA

7. In balance 3-ϕ circuit, the current and voltage coils of the wattmeter are connected as shown

in Fig. 2. Show that 3 times of wattmeter reading equals the total reactive power consumed

by the load. Q7 Ans: To be derived

8. For the circuit shown below, calculate the following, if Z1= (3+j4) ohm, Z2= (4+j3) ohm Z3=

5 ohm, neglect line impedance between load and source.

a. Load phase currents

b. Line currents

c. Source phase currents

d. Complex power in each phase of the load

Q8 Ans: a) CAI = (72-j96)A, ABI = (-110.3-j47.1)A, BCI = (-60+j103.9)A,

b) aCI =(132-j200)A, bAI = (50+j151)A, cBI = (50+j151)A

c) baI =(27.2-j117)A, cbI = (77.5-j34)A, acI = (-140.8-j83)A

d) ACS =(43.2+j5.76)*1e4 A, CBS = (5.76+j4.32)*1e4 A, BAS = 7.2*1e4 A

CC

PC

Z

Z

Z

Source

a

b

c

A

B

C

N

nj

Z1 Z3

Z2 120600

0600120600

A

C

B

a

c b

aCI

bAI

cBI