• # question_answer In a circuit L, C and R are connected in series with an alternating voltage source of frequency f The current leads the voltage by ${{45}^{o}}$. The value of C is           A)  $\frac{1}{\pi (2\pi fL-R)}$                           B)  $\frac{1}{2\pi (2\pi fL-R)}$C)  $\frac{1}{\pi f(2\pi fL+R)}$      D)  $\frac{1}{2\pi f(2\pi fL+R)}$

From figure, $\tan {{45}^{o}}=\frac{\frac{1}{\omega C}-\omega L}{R}$ $\Rightarrow$ $\frac{1}{\omega C}-\omega L=R\Rightarrow \frac{1}{\omega C}=R+\omega L$ $C=\frac{1}{\omega (R+\omega )}=\frac{1}{2\pi f\,(R+2\pi fL)}$