L, C and R are in series with an AC source of frequency f. The current leads the applied voltage by 45°. Express the capacitance C in terms of f, L and R.
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Question

L, C and R are in series with an AC source of frequency f. The current leads the applied voltage by 45°. Express the capacitance C in terms of f, L and R.

G1 Physics · Accepted Answer

Step 1: If current leads applied voltage by 45°, the series circuit is net capacitive and tan45°=(X(C)−X(L))/R=1. Step 2: Thus 1/(ωC)−ωL=R; rearrange to 1/(ωC)=R+ωL. Step 3: C=1/[ω(R+ωL)]=1/[2πf(R+2πfL)]. This matches D. Final answer: (D) 1/[2πf(2πfL + R)].