In the given circuit the AC source has ω = 100 rad s-1. Considering… | JEE Main 2021 (26 Aug, Shift 2)

Q9JEE Main 2021 · 26 AUG · SHIFT 2Medium

Parallel AC Circuits

In the given circuit the AC source has $\omega$ = 100 rad s-1. Considering the inductor and capacitor to be ideal, what will be the current I flowing through the circuit?

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Answer: (b)

C branch: $X_C = \frac{1}{100\times10^{-4}} = 100\ \Omega$ , $Z_1 = 100\sqrt{2}$ , $I_1 = \sqrt{2}$ A leading $V$ by $45^\circ$ .
L branch: $X_L = 100\times0.5 = 50\ \Omega$ , $Z_2 = 50\sqrt{2}$ , $I_2 = 2\sqrt{2}$ A lagging $V$ by $45^\circ$ .
$I_1$ and $I_2$ are $90^\circ$ apart: $I = \sqrt{I_1^2 + I_2^2} = \sqrt{2+8} = \sqrt{10}$
$I \approx 3.16$ A, so the answer is (b).

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