Q. 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°. The value of C is :
A) 1/[2πf(2πfL + R)]
B) 1/[πf(2πfL + R)]
C) 1/[2πf(2πfL − R)]
D) 1/[πf(2πfL − R)]
Explanation
[Solution from source] Current leading the voltage means the circuit is net capacitive: tan 45° = (X_C − X_L)/R = 1, so X_C = X_L + R. 1/(2πfC) = 2πfL + R gives C = 1/[2πf(2πfL + R)]. The form with (2πfL − R) would come from X_C = X_L − R, which makes the circuit inductive with current lagging. Answer (1).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.