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JEE Main 2021 (27 Jul, Shift 1) · RL and RC Series Circuits

RL and RC Series Circuits question from JEE Main 2021 (27 Jul, Shift 1)

Q40JEE Main 2021 · 27 JUL · SHIFT 1Medium

RL and RC Series Circuits

A 0.07 H inductor and a 12Ω\Omega resistor are connected in series to a 220V, 50 Hz ac source. The approximate current in the circuit and the phase angle between current and source voltage are respectively. [Take π\pi as 227\frac{22}{7} ]

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Answer: (a)

  1. XL=2πfL=2×227×50×0.07=22 ΩX_L = 2\pi f L = 2 \times \frac{22}{7} \times 50 \times 0.07 = 22\ \Omega
  2. Z=122+222=628≈25.1 ΩZ = \sqrt{12^2 + 22^2} = \sqrt{628} \approx 25.1\ \Omega
  3. I=22025.1≈8.8 AI = \frac{220}{25.1} \approx 8.8\text{ A}, tan⁡ϕ=2212=116\tan\phi = \frac{22}{12} = \frac{11}{6}
  4. So the answer is (a) 8.8 A and tan⁡−1(116)\tan^{-1}\left(\frac{11}{6}\right).
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