Question

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. $\bigg(\frac{(1)}{(2πf(2πfL + R)}\bigg)$
• B. $\bigg(\frac{(1)}{(πf(2πfL + R)}\bigg)$
• C. $\bigg(\frac{(1)}{(2πf(2πfL - R)}\bigg)$
• D. $\bigg(\frac{(1)}{(πf(2πfL - R)}\bigg)$

Answer 1

Answer: (C)

$\bigg(\frac{(1)}{(2πf(2πfL - R)}\bigg)$

Answer 2

tan $\phi$ = $\frac{X_C-X_L}{R}$

The current leads voltage by 450,

∴tan 45=$\frac{\frac{1}{2πfc} −2πfL}{R}$

$\Rightarrow$ C= $\frac{1}{2πf(2πfL+R)}$

Therefore, the correct option is (C): $\frac{1}{2πf(2πfL+R)}$