In a circuit L, C and R are connected in series with an alternating voltage of frequency f. the current leads the voltage by $45^\circ$. The value of C is ______.

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In a circuit L, C and R are connected in series with an alternating voltage of frequency f. the current leads the voltage by $45^\circ$. The value of C is 1/(2$\pi$f(2$\pi$fL + R)). Explanation: Let, Inductance = L Conductance = C Resistance = R Frequency = f Phase Difference between current and voltage = $\therefore$ tan phi = (X_L - X_C)/R ...(1) The current leads the voltage by $45^\circ$ Therefore, phi = $45^\circ$ tan phi = tan $45^\circ$ = 1 ...(2) Put the values in equation (1) and (2) and calculate: $\therefore$ (X_L - X_C)/R = -1 X_L - X_C = - R X_C = X_L + R 1/(2pifC) = 2pifL + R C = 1/(2pif(2pifL + R))

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