Question

In a circuit L, C and R are connected in series with an alternating voltage source of frequency v. The current leads the voltage by ${45}^0$. The value of C is

• A. $\frac{1}{\pi v(2\pi vL-R)}$
• B. $\frac{1}{2\pi v(2\pi vL-R)}$
• C. $\frac{1}{\pi v(2\pi vL+R)}$
• D. $\frac{1}{2\pi v(2\pi vL+R)}$

Answer 1

The correct option is D $\frac{1}{2\pi v(2\pi vL+R)}$

$\tan {45}^{\circ }=\frac{X_C-X_L}{R}$

$R=X_C-X_L$

$R=\frac{1}{2\pi \nu C}-2\pi \nu L$

$R+2\pi \nu L=\frac{1}{2\pi \nu C}$

$C=\frac{1}{2\pi \nu (R+2\pi \nu L)}$