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MHT CET 2026 (19 Apr, Shift 1) · Series LCR Circuit

Series LCR Circuit question from MHT CET 2026 (19 Apr, Shift 1)

Q7MHT CET 2026 · 19 APR · SHIFT 1Medium

Series LCR Circuit

For a series LCR circuit inductive reactance XLX_L is equal to resistance RR and also equal to twice the capacitive reactance XCX_C. The impedance of the circuit and the phase difference between voltage V and current i are respectively

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Answer: (c)

  1. XL=RX_L = R, XC=R2X_C = \frac{R}{2}, so XL−XC=R2X_L - X_C = \frac{R}{2}.
  2. Z=R2+R24=5R2Z = \sqrt{R^2 + \frac{R^2}{4}} = \frac{\sqrt{5}R}{2}
  3. tan⁡ϕ=XL−XCR=12⇒ϕ=tan⁡−1(12)\tan\phi = \frac{X_L - X_C}{R} = \frac{1}{2} \Rightarrow \phi = \tan^{-1}\left(\frac{1}{2}\right)
  4. So the answer is (c).
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