JEE Main · 2023 · 31 Jan 2023 · Shift 1 · Alternating Current

An inductor of 0.5 mH, a capacitor of

20 μ F

and resistance of

20Ω

are connected in series with a 220 V ac source. If the current is in phase with the emf, the amplitude of current of the circuit is

x A

. The value of x is -

Answer: 242

Solution

The current is in phase with the source only at resonance, where the inductive and capacitive reactances cancel and the impedance equals the resistance,

Z = R = 20 Ω

. The rms current is then

I_{r m s} = \frac{V _{r m s}}{R} = \frac{220}{20} = 11

A, and the peak current is

I_{0} = 2 I_{r m s} = 112

A. Writing this as

x

gives

x = (112)^{2} = 121 \times 2 = 242

JEE Main · 2023 · 31 Jan 2023 · Shift 1 · Integer answer

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