The voltage across the circuit in the figure and the current through it, are given by the following expressions: v(t)=5-10 \cos (\omega t+60^{\circ}) {v} i(t)=5+X \cos (\omega t) {A} where, \omega=100 \pi radian/s. If the average power delivered to the circuit is zero, then the value of {X} (in ampere) is (upto 2 decimal places).

GATE Electrical Engineering (EE) 2018 Solved Paper

Question : 40 of 65

Marks: +1, -0

The voltage across the circuit in the figure and the current through it, are given by the following expressions:

v(t)=5-10 \cos (ω t+60^{∘}) {v}

i(t)=5+X \cos (ω t) {A}

where,

ω=100 π

radian/s. If the average power delivered to the circuit is zero, then the value of

{X}

(in ampere) is (upto 2 decimal places).

Solution:

For power calculation same frequency terms must be used in both voltage and current.

P=V_{0} I_{0}+\;{1}/{2} V_{1} I_{1} \cos (θ_{v}-θ_{i})

V_{1}=-10 \cos (ω t+60^{∘})=10 \cos (ω t-120^{∘})

I_{1}=X \cos (ω t)

P=5 × 5+\;{1}/{2} × 10 × X \cos (120)=0

25+5 X \cos (120)=0

X=10

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