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GATE 2016 EE – Question 64

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 circuit below is excited by a sinusoidal source. The value of R, in $\Omega$, for which the admittance of the circuit becomes a pure conductance at all frequencies is ________.

A sinusoidal source feeds two parallel branches. One branch has a 100 μF capacitor in series with a resistor R. The other has a 0.02 H inductor in series with a resistor R.

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Correct answer: 14 to 14.2

Explanation

The admittance is $Y = \frac{1}{R + \frac{1}{j\omega C}} + \frac{1}{R + j\omega L}$. For this to be real at every frequency, the two branches must satisfy $R^2 = \frac{L}{C}$. Then $R = \sqrt{\frac{0.02}{100 \times 10^{-6}}} = \sqrt{200} = 14.14\ \Omega$.