GATE 2022 EE – Question 27

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 · 1 mark · Numerical answer

An inductor having a $Q$-factor of 60 is connected in series with a capacitor having a $Q$-factor of 240. The overall $Q$-factor of the circuit is ________. (round off to nearest integer)

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Correct answer: 48

Explanation

At resonance the reactances are equal, $X$. The series resistances are $R_L=\frac{X}{60}$ and $R_C=\frac{X}{240}$, so $Q=\frac{X}{R_L+R_C}=\frac{1}{\frac1{60}+\frac1{240}}=\frac{240}{5}=48$.