An RLC series circuit has R =2 Ω, C = 20 μF and the inductance is adjusted such that the voltage across the resistance is maximum. If the applied voltage is 10 V at a frequency of 1000 rad/sec, then find the value of inductance L. 

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SSC JE Electrical 4 Dec 2023 Official Paper II
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  1. 0.25 H
  2. 0.025 H
  3. 0.05 H
  4. 0.005 H

Answer (Detailed Solution Below)

Option 3 : 0.05 H
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Detailed Solution

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Concept:

  • For a series RLC circuit at resonance, the inductive reactance becomes equal to the capacitive reactance.
  • Thus, at the time of resonance, the circuit behaves as a purely resistive circuit.
  • The value of resonant frequency is given by:

           \(ω_c=\frac{1}{\sqrt{LC}}~rad/sec\)

Calculation:

For the given question; R = 2 Ω, ω= 1000 rad/sec, C = 20 μF

\(ω_c=\frac{1}{\sqrt{LC}}~rad/sec\)

\(1000= \;\frac{1}{{\sqrt {L \times {{20}^{ - 6}}}}}\)

⇒ L = 0.05 H

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