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A series LCR circuit has L=0.01 H, R=10 Ω and C=1 μF, connected to an a.c. voltage of amplitude 50 V. At a frequency 60% lower than the resonant frequency, the current amplitude is approximately

Asked in JEE Main 27th July 2nd Shift 2022 · Current and voltage at resonance

Answer: (3) 238 mA

Step-by-step solution

ω₀=1/(√LC)=1/(√0.01×10⁻⁶)=10⁴ rad/s.

60% lower: ω=0.4 ω₀=4000 rad/s.

X_L=ω L=40 Ω, X_C=1/(ω C)=250 Ω.

Z=√10²+(40-250)²=√44200≈210 Ω.

I₀=(50)/(210)≈0.238 A=238 mA.

Why the other options are wrong

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