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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

1. 1 / πf(2πfL − R)
2. 1 / 2πf(2πfL − R)
3. 1 / πf(2πfL + R)
4. 1 / 2πf(2πfL + R)

Correct answer: 1 / 2πf(2πfL − R)

Solution

For the current to lead the voltage by 45°, the circuit must be in a condition where the net reactance (X_L - X_C) equals the resistance (R). Using the formula for capacitive reactance, X_C = 1 / (2πfC), and solving for C, we get the correct expression as 1 / 2πf(2πfL − R).

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