A series LCR circuit with resistance R is connected to an alternating source of emf. At the resonant frequency, the current amplitude in the circuit is I₀ . At a different frequency ₁ , the current amplitude is observed to be I₀ 5 . The magnitude of the net reactance of the circuit at frequency ₁ is

Step-by-step solution

At the resonant frequency, the impedance is purely resistive ( Z = R ). The current amplitude is given by: I₀ = E₀ R At frequency ₁ , the impedance of the circuit is Z₁ = R^2 + X^2 , where X is the net reactance. The current amplitude at this frequency is I₁ = E₀ Z₁ . Given that I₁ = I₀ 5 , we can write: E₀ Z₁ = 1 5 ( E₀ R ) Z₁ = 5 R Squaring both sides and substituting the expression for Z₁ : R^2 + X^2 = 5R^2 X^2 = 4R^2 X = 2R Answer: 2R