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Punjab Medical Punjab - MET Solved Paper-2010

  • question_answer
    An inductor\[L,\,\,a\]capacitor of\[20\mu F\]and a resistor of \[10\Omega \] are connected in series with an AC source of frequency\[50Hz\]. If the current is in phase with the voltage, then the inductance of the inductor is

    A) \[2.00H\]                            

    B) \[0.51H\]

    C) \[1.5H\]                               

    D) \[0.99H\]

    Correct Answer: B

    Solution :

    In an\[L-C-R\]circuit, the current and the voltage are in phase\[(\phi =0)\], when                 \[\tan \phi =\frac{\omega L-\frac{1}{\omega C}}{R}=0\] or            \[\omega L=\frac{1}{\omega C}\] or            \[L=\frac{1}{{{\omega }^{2}}C}\] Here,\[\omega =2\pi f=2\times 3.14\times 50{{s}^{-1}}=314{{s}^{-1}}\] and        \[C=20\mu F=20\times {{10}^{-6}}F\] \[\therefore \]  \[L=\frac{1}{(314{{s}^{-1}})\times (20\times {{10}^{-6}}F)}=0.51\,\,H\]


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