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GATE 2018 EE – Question 65

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 $v(t)$ across the terminals $a$ and $b$ as shown in the figure, is a sinusoidal voltage having a frequency $\omega=100$ radian/s. When the inductor current $i(t)$ is in phase with the voltage $v(t)$, the magnitude of the impedance $Z$ (in $\Omega$) seen between the terminals $a$ and $b$ is ________ (up to 2 decimal places).

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Correct answer: 50

Explanation

The parallel $R$-$C$ part is $\frac{100}{1+j100\times100\ \mu\text{F}\times100}=\frac{100}{1+j}=50-j50\ \Omega$. For the current to be in phase with $v(t)$ the total impedance must be real, so $\omega L=50\ \Omega$ cancels the $-j50$. Then $Z=50\ \Omega$.