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MHT CET 2024 (15 May, Shift 1) · RL and RC Series Circuits

RL and RC Series Circuits question from MHT CET 2024 (15 May, Shift 1)

Q27MHT CET 2024 · 15 MAY · SHIFT 1Medium

RL and RC Series Circuits

When a coil is connected to a d.c. source of e.m.f. 12 volt; then the current of 4 A flows in it. If the same coil is connected to a 12 volt, 50 Hz a.c. source, then the current flowing in it is 2.4 A. Then self-inductance of the coil will be

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Answer: (c)

  1. DC sees only resistance: R=124=3 ΩR = \frac{12}{4} = 3\ \Omega.
  2. AC: Z=122.4=5 ΩZ = \frac{12}{2.4} = 5\ \Omega, so XL=52−32=4 ΩX_L = \sqrt{5^2 - 3^2} = 4\ \Omega.
  3. L=XL2πf=4100π=4π×10−2 HL = \frac{X_L}{2\pi f} = \frac{4}{100\pi} = \frac{4}{\pi} \times 10^{-2}\text{ H}
  4. So the answer is (c) 4π×10−2\frac{4}{\pi} \times 10^{-2} H.
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