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JEE Main 2024 (5 Apr, Shift 1) · Series LCR Circuit

Series LCR Circuit question from JEE Main 2024 (5 Apr, Shift 1)

Q26JEE Main 2024 · 5 APR · SHIFT 1Medium

Series LCR Circuit

An ac source is connected in given series LCR circuit. The rms potential difference across the capacitor of 20 μF20\ \mu\text{F} is __________ V.

Figure

Numerical answer type. Work it out, then open the answer.

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Answer: 50

  1. ω=100\omega = 100 rad/s, Vrms=50V_{rms} = 50 V
  2. XL=100×1=100 ΩX_L = 100 \times 1 = 100\ \Omega, XC=1100×20×10−6=500 ΩX_C = \frac{1}{100 \times 20 \times 10^{-6}} = 500\ \Omega
  3. Z=3002+4002=500 Ω⇒Irms=50500=0.1Z = \sqrt{300^2 + 400^2} = 500\ \Omega \Rightarrow I_{rms} = \frac{50}{500} = 0.1 A
  4. VC=IrmsXC=0.1×500=50V_C = I_{rms} X_C = 0.1 \times 500 = 50 V
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