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EET 101 ELECTRIC CIRCUIT I
TUTORIAL 4 – QUESTIONS
AC POWER ANALYSIS
1.
Calculate the instantaneous power and the average power if;
v  339 cos100t V

Ans:
2.

i  18 sin 100t  60 A
and


p  2642.2  3051cos 200t  30 W ;
P  2642.2 W
Calculate the power delivered by the voltage source v(t) in Figure 1 if;


vt   170 cos 120t  53 V
30 
10 
132.6 F
v (t )
66.3 mH
Figure 1
Ans:
3.
P  174.5 W
Compute the power dissipated by R2 in the Figure 2. Assume that the magnitude 5 A given
for Is represents its r.m.s. value.
XC
-j 8 
I1
+ Vo A
B
+
R1
12 
Is
50
5Vo
I2
XL
j 16 
_
I1
C
Figure 2
I3
R2
24 
Ans:
P2  367.38 W
4.
If the voltage source Vs in Figure 3 has a value of 24030 Vrms, find;
(a)
(b)
(c)
the power factor of the circuit;
the average active power dissipated by the circuit; and
the total apparent power supplied by the source.
R1
R2
10 
24 
XC
-j 20 
R3
32 
XL
j 16 
Vs
p. f .  0.75 lagging ; P  1.83 kW ; S  2.44 kVA
Ans:
5.
The power dissipated/absorbed by each element in Figure 4 is as indicated in the figure.
Calculate;
(a)
(b)
(c)
the apparent power delivered by the source;
the current drawn from the source; and
the power factor of the circuit.
176 W
120 Vrms
0
1.145 kW
1.68 kVAr
Ans:
6.
Figure 3
Figure 4
2.29 kVAr
S  1.455 kVA ;
I  12.13 A ;
p. f  0.908
Three loads A, B and C when connected across 12030 Vrms as shown in Figure 5, received
and dissipated power as indicated. Calculate;
(a)
(b)
I; and
the power factor of the combination.
I
+
V
= 120 30 Vrms
_
LOAD A
4 kVA @ 0.8 pf
leading
LOAD B
2.4 kVA @ 0.6
pf lagging
LOAD C
Inductive
1 kW; 500 VAR
Figure 5
I  4729.8 A ;
Ans:
7.
pf  1
Compute Vo and the input power factor for the circuit in Figure 6.
+
910
18 kW
0.75 pf lagging
Vo
12 kW
0.86 pf lagging
Figure 6
_
Ans:
pf  0.793 lagging
Vo  415.437.5 V ;
THREE-PHASE CIRCUITS
8.
If Vab  400 V in a balanced Y-connected three-phase generator, find the phase voltages,
assuming the phase sequence is;
(a)
abc
(b)
acb
Ans:
Van  231  30  V; Vbn  231  150  V; Vcn  231  90  V
Van  23130 V;
9.
Vbn  231150 V;
Vcn  231  90 V
For a balanced three-phase circuit, Vbn  208130 V ; Vcn  20810 V . Determine
the phase sequence and Van .
Ans:
Van  208250 V  208  110 V
10.
For the three-phase Y-connected load in Figure 7, determine the time-domain expression
for the line-to-line voltages v AB , vBC and vCA if;


 150 cost  88  V ;
 150 cost  152  V
v AN  150 cos t  32 V ;
vBN
vCN

and

Ans:




vAB  260 cos t  62 V
vBC  260 cos t  58 V


vCA  260 cos t  178 V
A
B
v BN
v AN
N
Figure 7
v CN
C
3-PHASE Y-CONNECTED LOAD
11.
Find the line currents I a , I b and I c in the three-phase circuit shown in Figure 8.
Ia
3
6 - j8 
4400 V
Figure 8
6 - j8 
4400 V
6 - j8 
Ib
4400 V
3
3
Ic
Ans:
12.
I a  36.5441.6 A; I b  36.54  78.4 A;
I c  36.54161.4 A
For the balanced three-phase - in Figure 9, calculate;
(a)
(b)
(c)
the magnitude of line current;
the magnitude of the load phase current; and
the average power dissipated by the load.
Ans:
I L  17.18 A; I P  9.92 A; PL  2.657 kW
LINE
SOURCE
LOAD
2
1100 V
9 + j 12 
1100 V
2
9 + j 12 
Figure 9
9 + j 12 
1100 V
2
13.
The load shown in Figure 10 is connected to a balanced three-phase source with a line
voltage of 415 V through terminals a, b and c. Calculate the magnitude of the line current IL.
Ans:
IL
I L  25.1 A
1.2 + j 1 
a
415 V
1.2 + j 1 
b
30 + j 18 
415 V
16 - j 9 
16 - j 9 
415 V
30 + j 18 
30 + j 18 
16 - j 9 
1.2 + j 1 
c
Figure 10
14.
If Vbn  220  60 V in the network shown in Figure 11, find
(a)
the load phase currents I AB , I BC and I CA ;
(b)
the line currents I a , I b and I c .
Ans:
I AB  25.437 A;
and
I BC  25.4  83 A; I CA  25.4157 A
I a  447 A; I b  44  113 A;
I c  44127 A
Ia
a
A
3-phase,
Y-connected
generator
IAB
9
j 12 
j 12 
C
j 12 
9
B
(+) phase
sequence
Figure 11
ICA
IBC
Ib
b
9
Ic
c
Find the line currents I a , I b and I c in Figure 12 if;
15.
Zl  2  ,
ZY  4  j6 
Z  12  j15 
and
I a  15.541.6 A;
Ans:
Zl
a
I b15.54  118.4 A; I c  15.54121.6 A
Ia
A
ZY
Z
2080 V
Z
2080 V
Zl
b
c
C
B
2080 V
Zl
ZY
ZY
Ib
Z
Ic
Figure 12
16.
Find the line currents I a , I b and I c in Figure 13.
a
3 + j2 
Ia
10 - j 8 
44010 V
3 + j2 
44030 V
Ib
10 - j 8 
Figure 13
b
10 - j 8 
44010 V
3 + j2 
c
Ic
Ans:
I a  17.744.8 A;
I b  17.74  115.2 A;
I c  17.74124.8 A
17.
Three identical loads each comprising a 42– resistor in series with a 162.4–mH inductor
are delta-connected across a star-connected three–phase source of 415–V; 50–Hz through three
transmission lines. Each of these lines may be represented by a resistance of 1  in series with an
inductance of 4.8 mH.
(a)
(b)
(c)
(d)
Draw the circuit diagram of the system in frequency domain.
Calculate all the line and phase currents of the system.
Calculate the total active power, reactive power, complex power and apparent
power delivered to the load.
Show the approximate positions of the phasors for the line and phase currents on
the phasors of the line voltages given in Figure 14.
Assume positive phase sequence and the line voltage Vab  4150 (r.m.s. value)
Ans:
(b)
(c)
I AB  5.81  51 A; I BC  5.81  171 A; I CA  5.8169  A
P  4.253 kW; Q  5.165 kVAR;
S  4.253  j5.165 kVA;
S  6.69 kVA
Vca
Vab
120
120
Figure 14
Vbc
18.
A three-phase delta-connected source delivers a total of 5.8 kVA to a balanced Yconnected load of power factor 0.8 lagging. The line voltage of the source is 381 V. Draw the
circuit diagram of the system and compute;
(a)
(b)
(c)
(d)
(e)
the load phase voltages;
the line currents;
the source phase currents ;
the average active power and reactive power supplied to each phase of the load;
the load impedance ZY of each phase.
Assume positive phase sequence with Vab  3810 V
Ans:
(b)
VAN  220  30 V; VBN  220  150 V; VCN  22090 V
(c)
I a  8.79  67 A;
(d)
Pp  1547 W; Q p  1160 VAR
I b  8.79173 A;
(e)
I c  8.7953 A
ZY  20  j15   2537 
19.
Three identical loads, each 60  j 30  , are delta-connected across a three-phase source.
The source line voltage is 398 V rms. Another three identical loads, each 40  j10  , are Yconnected across the same source at the same points. Draw the circuit diagram of the system and
determine;
(a)
(b)
(c)
the magnitude of the line current;
the total real, imaginary and complex power supplied to the two loads;
the power factor of the two loads combined.
Ans:
20.
(a)
I L  15.76  22.2 A
(b)
P  10.06 kW ;
(c)
Power factor  0.927 lagging
Q  4.107 kVAR ;
S  10.86622.2 kVA
Find the real power absorbed the load in Figure 15.
Ans:
P  432 W
5
4
-j 6 
1000 V
1000 V
1000 V
j3 
8
5
5
10 
Figure 15