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The resonance frequency of LCR series a.c. circuit is f 0 . Now the capacitance is made 4 times, then the new resonance frequency will become

Options

  1. Af 0 4
  2. B2 f 0
  3. Cf 0
  4. Df 0 2

Correct answer

D. f 0 2

Step-by-step solution

In LCR series circuit, resonance frequency f 0 is given by L ω = 1 C ω ⇒ ω 2 = 1 L C ∴ ω = 1 L C = 2 π f 0 ∴ f 0 = 1 2 π L C or f 0 ∝ 1 C When the capacitance of the circuit is made 4 times, its resonant frequency become f 0 ′ ∴ f 0 ′ f 0 = C 4 C or f 0 ′ = f 0 2

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