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In a circuit, L,C and R are connected in series with an alternating voltage source

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 45⁰. The value of C is

Options

(a) 1/πf(2πfL+R)
(b) 1/πf(2πfL-R)
(c) 1/2πf(2πfL-R)
(d) 1/2πf(2πfL+R)

Correct Answer:

1/2πf(2πfL+R)

Explanation:

The phase difference ɸ between current and voltage is given by

tan ɸ = (Xʟ – Xc) / R

(Xʟ – Xc) / R = tan 45° = 1 ⇒ Xc = X⇒ + R

1 / 2πfC = 2πfL + R

Therefore, C = 1 / 2πf(2πfL + R)

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