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JIPMER 2007
Exam
JIPMER
Year
2007
Subject
Physics
Chapter
Alternating Current

JIPMER 2007 · Physics · Alternating Current

In a circuit, L, C and R are connected in series with an...

In a circuit, L,CL, C and RR are connected in series with an alternating voltage source of frequency ff. The current leads the voltage by 45∘45^{\circ}. The value of CC is

Options

  1. A12πf(2πfL+R)\frac{1}{2 \pi f(2 \pi f L+R)}
  2. B1πf(2πfL+R)\frac{1}{\pi f(2 \pi f L+R)}
  3. C12πf(2πfL−R)\frac{1}{2 \pi f(2 \pi f L-R)}
  4. D1πf(2πfL−R)\frac{1}{\pi f(2 \pi f L-R)}

Correct answer

C. 12πf(2πfL−R)\frac{1}{2 \pi f(2 \pi f L-R)}

Step-by-step solution

tan⁡ϕ=XC−XLRtan⁡(π4)=1ωC−ωLRR=1ωC−ωL(R+2πfL)=12πfCor C=12πf(R+2πfL)\begin{aligned} & \tan \phi=\frac{X_C-X_L}{R} \\ & \tan \left(\frac{\pi}{4}\right)=\frac{\frac{1}{\omega C}-\omega L}{R} \\ & R=\frac{1}{\omega C}-\omega L \\ & (R+2 \pi f L)=\frac{1}{2 \pi f C} \\ & \text{or } C=\frac{1}{2 \pi f(R+2 \pi f L)} \end{aligned})$
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