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A series LCR circuit is fed by a 200 V, 50 Hz a.c. signal. If the voltage across the inductor (L=10 mH) is 31.4 V, the current in the circuit is

Asked in JEE Main 5th April 2nd Shift 2024 · Voltages across the elements

(1) 68 A
(2) 10 A
(3) 63 A
(4) 10 mA

Answer: (2) 10 A

Step-by-step solution

X_L=ω L=2π f L=2π(50)(0.01)=3.14 Ω.

Only the inductor voltage acts across X_L: I=(V_L)/(X_L)=(31.4)/(3.14)=10 A.

Why the other options are wrong

(1) Uses the 200 V source across L instead of the 31.4 V actually across it.
(3) Drops the 2π, taking X_L=fL=0.5 Ω, so 31.4/0.5≈63.
(4) Inflates X_L by a factor 10³ through a reactance unit slip.

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