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MHT CET 2024 (11 May, Shift 1) · Series LCR Circuit

Series LCR Circuit question from MHT CET 2024 (11 May, Shift 1)

Q29MHT CET 2024 · 11 MAY · SHIFT 1Medium

Series LCR Circuit

With an alternating voltage source frequency ' f ', inductor ' LL ', capacitor ' CC ' and resistance ' RR ' are connected in series. The voltage leads the current by 45∘45^\circ. The value of ' LL ' is (tan⁡45∘=1)(\tan 45^\circ = 1)

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Answer: (a)

  1. Voltage leads by 45∘45^\circ: tan⁡45∘=XL−XCR⇒XL=XC+R\tan 45^\circ = \dfrac{X_L - X_C}{R} \Rightarrow X_L = X_C + R.
  2. 2πfL=12πfC+R=1+2πfCR2πfC2\pi fL = \dfrac{1}{2\pi fC} + R = \dfrac{1 + 2\pi fCR}{2\pi fC}
  3. L=1+2πfCR4π2f2CL = \dfrac{1 + 2\pi fCR}{4\pi^2f^2C}
  4. So the answer is (a).
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