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NEET 2005
Exam
NEET
Year
2005
Subject
Physics
Chapter
Alternating Current

NEET 2005 · Physics · Alternating Current

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

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

Options

  1. A1πf(2πf(L−R)\frac{1}{\pi f(2 \pi f(L-R)}
  2. B12πf(2πfL−R)\frac{1}{2 \pi f(2 \pi f L-R)}
  3. C1πf(2πfL+R)\frac{1}{\pi f(2 \pi f L+R)}
  4. D12πf(2πfL+R)\frac{1}{2 \pi f(2 \pi f L+R)}

Correct answer

D. 12πf(2πfL+R)\frac{1}{2 \pi f(2 \pi f L+R)}

Step-by-step solution

tan⁡ϕ=XC−XLRtan⁡(π4)=1ωC−ωLR⇒R=1ωC−\omegaL(R+2\pifL)=22πfCC=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}\\ \Rightarrow \quad R & =\frac{1}{\omega C}-\omegaL \\ (R+2 \pif L) & =\frac{2}{2 \pi f C}\\ C & =\frac{1}{2 \pi f(R+2 \pi f L)} \end{aligned}
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