The figure given below shows an LCR series circuit with two switches S₁ and S₂ . When switch S₁ is closed keeping S₂ open, the phase difference ( ) between the current and source voltage is 30° and phase difference is 60° when S₂ is closed keeping S₁ open. The value of (3L₁ - L₂) is _______ H.

Step-by-step solution

From the source v = V₀ (300t) , the angular frequency is = 300 rad/s . Capacitance C = 100 F = 10⁻⁴ F , so X_C = 1 C . Case 1 ( S₁ closed, S₂ open): Closing S₁ short-circuits L₂ , leaving an LCR series circuit with C , R and L₁ . With phase difference ₁ = 30^ : 30^ = L₁ - X_C R 1 3 = L₁ - X_C R R = 3 ,( L₁ - X_C) ... (1) Case 2 ( S₂ closed, S₁ open): Closing S₂ short-circuits L₁ , leaving an LCR series circuit with C , R and L₂ . With phase difference ₂ = 60^ : 60^ = L₂ - X_C R 3 = L₂ - X_C R L₂ - X_C = R 3 ... (2)