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Q.

In a circuit, L, C and R are connected in series with an alternating voltage source of frequency f. The current lags the voltage by 450. The value of C is

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a

12πf(2πfL+R)

b

1πf(2πfL+R)

c

12πf(2πfL−R)

d

1πf(2πfL−R)

answer is C.

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Detailed Solution

tanϕ=ωL−1ωCRϕ being the angle by which the current lags the voltage.Given, ϕ=45∘∴ tan45∘=ωL−1ωCR⇒ 1=ωL−1ωCR⇒ R=ωL−1ωC⇒ C=1ω(ωL−R)=12πf(2πfL−R)
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