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JEE Main 2014 (9 Apr, Shift 1) · Series LCR Circuit

Series LCR Circuit question from JEE Main 2014 (9 Apr, Shift 1)

Q58JEE Main 2014 · 9 APR · SHIFT 1Medium

Series LCR Circuit

When the rms voltages VL, VC and VR are measured respectively across the inductor L, the capacitor C and the resistor R in a series LCR circuit connected to an AC source, it is found that the ratio VL: VC: VR = 1: 2: 3. If the rms voltage of the AC source is 100 V, then VR is close to:

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Answer: (c)

Let $V_L = x$ , $V_C = 2x$ , $V_R = 3x$ .
$100^2 = (3x)^2 + (x - 2x)^2 = 10x^2 \Rightarrow x = 10\sqrt{10} \approx 31.6$ V
$V_R = 3x \approx 95$ V, closest to 90 V.
So the answer is (c) 90 V.

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