ece320 hw1 solution
TRANSCRIPT
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7/26/2019 ECE320 HW1 Solution
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HOME WORK # 1 SOLUTIONS ECE 320
1. The circuit of figure below is excited by a 240-V, 60-Hz sinusoidal source. If FC 10= ,
determine:
(a)
The magnitude of currentI
(b) The average value of power dissipated by resistorR
= 10R
I1
I2I
C mHL 25=V
+
Solution:
(a) It is convenient to assume V on the reference. The two branch impedances are found as
( )1 6
1 1 1 9090 265.258 90
120 10 10j
C C
= = = =
Z
( )( )210 120 0.025 10 9.425 13.742 43.3R j L j j = + = + = + = Z
The branch current can now be determined.
1
1
240 00.905 90 A
265.258 90
VI
= = =
Z
2
2
240 017.465 43.3 A
13.742 43.3
VI
= = =
Z
Applying KCL,
1 2 0.905 90 17.465 43.3I I I= + = +
12.710 11.073 16.857 41.06 Aj= =
Hence,
16.857 AI=
(b) The power dissipated by Ris
( ) ( )22
2 17.465 10 3050.26 WRP I R= = =
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2. A set of balanced three-phase voltages is impressed on a balanced, three-phase, delta-
connected load. If = 07200abV V and = 012aI A. Determine:
(a) The phase current abI
(b) The total average power supplied to the load.
Solution:
Assume phase sequence.a b c
(a) The phase current abI
12 0
3 30 3 30
aab
II
= =
6.928 30 AabI =
(b) The total average power supplied to the load.
30ab abV I= = ,
( )( ) ( )3 cos 3 7200 12 cos 30 129.60 kWT L LP V I = = =
3. Capacitors C are added to the 60-Hz, three-phase network given below to correct the
input power factor to unity. Determine:
(a) The value of C
(b)
If V, find the total kVAR rating of the capacitor bank.480=VAB
C
C
C
A
B
C
4j
3
Solution:
(a) The R-Lbranches of the delta network can be converted to an equivalent wye network by
( )1 1
3 33 4Y j= = +ZZ
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In order for a unity PF to exist, the reactive power supplied by the capacitor of each phase
must equal the reactive power supplied to the inductor of each phase.2
2Y
Y
VCV L
Z
=
or( )
2 2 2 2 2
1
34/120
1273.2 F3 4
3 3 3 3
Y Y
Y
L LC
Z R L
= = = =
+ +
(b)
( )( )2
2 6 4803 3 120 1273.2 10 110.59 kVARs3
TQ CV = = =