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NEET Sample Paper NEET Sample Test Paper-37

  • question_answer
    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 \[\text{45 }\!\!{}^\circ\!\!\text{ }\]. The value of C is

    A) \[\frac{1}{2\pi f(2\pi fL+R)}\]

    B)  \[\frac{1}{\pi f(2\pi fL+R)}\]

    C)  \[\frac{1}{2f(2\pi fL-R)}\]

    D) \[\frac{1}{\pi f(2\pi fL-R)}\]

    Correct Answer: C

    Solution :

     \[\tan \phi =\frac{\omega L-\frac{1}{\omega C}}{R}\] \[\phi \]being the angle by which the current leads the voltage. Given, \[\phi ={{45}^{o}}\] \[\therefore \] \[\tan {{45}^{o}}=\frac{\omega L-\frac{1}{\omega C}}{R}\] \[\Rightarrow \] \[1=\frac{\omega L-\frac{1}{\omega C}}{R}\] \[\Rightarrow \] \[R=\omega L-\frac{1}{\omega C}\] \[\Rightarrow \] \[\omega C=\frac{1}{(\omega L-R)}\] \[\Rightarrow \] \[C=\frac{1}{\omega (\omega L-R)}=\frac{1}{2\pi f(2\pi fL-R)}\]


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