HNC Electrical Engineering Assignment

2019
HNC Electrical Engineering
Assignment
MODULE TITLE: ELECTRICAL AND ELECTRONIC
PRINCIPLES
TOPIC TITLE: CIRCUIT THEORY
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QUESTION I
Determine current flowing in the load by
(i) Applying Thevenin’s theorem
(ii) Applying the superposition theorem
(iii) By transforming the two voltage sources and their associated reactance into current
sources (and thus form a pair of Norton generators)
Solution
Part a
The root mean square values are given as,
V 1=415 ∠900
V 2=415 ∠00=415
The load impedance,
ZL=50 ohms @0.7 pf
Converting into a polar representation,
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ZL=34.999+ j 35.707 ohms
Using Thevenin theorem, the circuit is divided into two loops,
loo p1 =− j 4 ( I 1 )−35.002+ j35.705 ( I 2 )=− j 415
loo p2=− j 6 ( I 1 ) −35.002+ j 41.705 I 2=0
Part b
Implementing the Cramer’s rule,
¿ ( − j 4 ) ( 35.002+ j 41.705 ) − ( j 6 ) ( −35.002+ j 35.705 )
¿ ( 166.82− j140.008 )− ( 214.3+ j210.012 )
¿−47.41− j 350.02
In the first loop, a matrix is obtained,
¿ [− j 415 −35.002+ j35.705
0 35.002+ j 41.705 ]
Removing the load the circuit is as illustrated below,
The load impedance is given as,
Z= √ R2+ X2
The power factor is given as 0.7 and the resistance is 50 ohms.
cos θ=0.7
arctan ( 51.01
50 )=45.57
Z=50+i51.01
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