Solveeit Logo
Login

Question

Physics Question on LCR Circuit

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∘^{\circ}. The value of C is

A

1πf(2πfL−R)\frac{1}{\pi f(2\pi fL-R)}

B

12πf(2πfL−R)\frac{1}{2\pi f(2\pi fL-R)}

C

1πf(2πfL+R)\frac{1}{\pi f(2\pi fL+R)}

D

12πf(2πfL+R)\frac{1}{2\pi f(2\pi fL+R)}

Answer

12πf(2πfL+R)\frac{1}{2\pi f(2\pi fL+R)}

Explanation

Solution

tan ϕ=XC−XLRtan \, \phi=\frac{X_C-X_L}{R}
tan(π4)=1ωC−ωLRtan\big(\frac{\pi}{4}\big)=\frac{\frac{1}{\omega C}-\omega L}{R}
R=1ωC−ωLR=\frac{1}{\omega C}-\omega L
(R+2πfL)=12πfL(R+2\pi fL)=\frac{1}{2\pi fL}
or C=12πf(R+2πfL)C=\frac{1}{2\pi f(R+2\pi fL)}