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Alternating Current question

2005 · Q136
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Alternating Current question

2005 · Q136

NEETPhysicsAlternating CurrentMCQ+4 / −1
In a circuit L, C and R are connected in series with an alternating voltage source of frquency f.f.f. The current leads the voltage by 45o. The value of C is
  1. A
    1πf(2πf L−R){1 \over {\pi f\left( {2\pi f\,L - R} \right)}}πf(2πfL−R)1​
  2. B
    12πf(2πf L−R){1 \over {2\pi f\left( {2\pi f\,L - R} \right)}}2πf(2πfL−R)1​
  3. C
    1πf(2πf L+R){1 \over {\pi f\left( {2\pi f\,L + R} \right)}}πf(2πfL+R)1​
  4. D
    12πf(2πf L+R){1 \over {2\pi f\left( {2\pi f\,L + R} \right)}}2πf(2πfL+R)1​
View written solutionFree

Correct answer: D

tanϕ\phi ϕ = XC−XLR{{{X_C} - {X_L}} \over R}RXC​−XL​​

⇒\Rightarrow⇒ tan⁡(π4)=1ωC−ωLR\tan \left( {{\pi \over 4}} \right) = {{{1 \over {\omega C}} - \omega L} \over R}tan(4π​)=RωC1​−ωL​

⇒\Rightarrow⇒ R = 1ωC−ωL{{1 \over {\omega C}} - \omega L}ωC1​−ωL

⇒\Rightarrow⇒ R + 2π\pi πfL = 12πfC{1 \over {2\pi fC}}2πfC1​

⇒\Rightarrow⇒ C = 12πf(R+2πfL){1 \over {2\pi f\left( {R + 2\pi fL} \right)}}2πf(R+2πfL)1​

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