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JEE MainPhysicsAlternating Current

The graph of current amplitude versus angular frequency for two different series LCR circuits (A and B) shows that both curves peak at the exact same angular frequency. If the inductance of circuit A is 4 times the inductance of circuit B, the ratio of their capacitances C_A : C_B is :

Options

  1. A4 : 1
  2. B1 : 4
  3. C2 : 1
  4. D1 : 2

Correct answer

B. 1 : 4

Step-by-step solution

From the given description, both circuits have the same resonance frequency. Let the resonance frequency be ₀ . For a series LCR circuit, ₀ = 1 LC Since _ 0A = _ 0B , we have: 1 L_A C_A = 1 L_B C_B L_A C_A = L_B C_B Given L_A = 4 L_B , substituting this gives: 4 L_B C_A = L_B C_B C_A C_B = 1 4 Thus, the ratio C_A : C_B is 1 : 4 . Answer: 1 : 4

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