A coil with an internal resistance R = 100 , and an unknown inductance is connected to an AC source of angular frequency = 100 rad/s . In this state, the current lags the applied voltage by 45^ . A capacitor is then connected in series with the coil, which causes the resultant current to lead the applied voltage by 45^ . The value of the capacitance C is

Step-by-step solution

Initially, the circuit consists of a resistance and an inductance (RL circuit). The current lags the voltage by 45^ . Using the phase angle formula for an RL circuit: ₁ = X_L R 45^ = X_L 100 1 = X_L 100 X_L = 100 , When the capacitor is added in series, the circuit becomes an LCR circuit. The current now leads the voltage by 45^ , which means the circuit is capacitive in nature ( X_C > X_L ). Using the phase angle formula for this state: ₂ = X_C - X_L R 45^ = X_C - 100 100 1 = X_C - 100 100 X_C - 100 = 100 X_C = 20