GATE 2026 IN – Question 33
In the series RL circuit shown, the current through the resistor lags the AC source voltage by $45^\circ$. Let $R=100\pi\ \Omega$ and $L=2\ \mathrm H$. The frequency of the source is ________ Hz. (Rounded off to the nearest integer.)
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Correct answer: 25 to 25
Explanation
The series impedance is $Z=R+j\omega L$, so the phase lag satisfies $\tan\phi=\omega L/R$. At $\phi=45^\circ$, $\omega L=R$.
Therefore $f=\omega/(2\pi)=R/(2\pi L)=100\pi/(2\pi\times2)=25\ \mathrm{Hz}$. The answer is **25 Hz**.