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network problems!!

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Printed Date: 06Feb2025 at 3:18pm


Topic: network problems!!
Posted By: manju
Subject: network problems!!
Date Posted: 22Feb2007 at 11:55am
 GATE (91) PART B, PROBLEM-13

Soln:- The above problem has really puzzled me,
Equivalent ckt consists of a 50 source opposing a 10-60 source and series resistance of (6+4).
This gives i = (10-60 - 50 )/(6+4) = -j0.866 amps (anticlockwise sense)

Using voltage conjugate VI*,

Power 50 source………….( 50 )( -j0.866 )* (absorbed)
= j(4.33)

Power 10-60 source……….(10-60 )( -j0.866 )* (generated)
= 7.5 + j(4.33)

It indicates 7.5 W is dissipated in the (6+4).
Which gives, P6 = 4.5 W
P4 = 3.0 W

But the actual answer is different,

Power dissipated in the resistors = 0 (since real part of current is zero)

Power delivered by 50 source = 2.5W
Power delivered by 10-60 source = 10W



Replies:
Posted By: vikram_roy
Date Posted: 03Mar2008 at 3:56am
the answer will be zero as the reactive current passing through resistors do not dissipate power it has a positive power consumption in t/2 and negative power return in the next half i.e. t/2 t being the time period.



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