The GATE Grind

GATE 2018 EE – Question 58

Electric Circuits · Transient response of DC and AC networks, sinusoidal steady-state analysis, resonance, two port networks, balanced three phase circuits, star-delta transformation, complex power and power factor in AC circuits · 2 marks · Numerical answer

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 ________ (up to 2 decimal places).

Diagram for GATE 2018 EE question 58

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: 10

Explanation

The average power is $P=5\times5+\frac12(-10)(X)\cos60^\circ=25-2.5X$. Setting it to zero gives $X=10$ A.