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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2011

  • question_answer
        In an AC circuit the potential difference V and current I are given respectively by \[V=100\sin (100t)volt\] and      \[I=100\sin \left( 100t+\frac{\pi }{3} \right)mA\] The power dissipated in the circuit will be

    A)  \[{{10}^{4}}W\]               

    B)  \[10W\]

    C)  \[2.5\text{ }W\]              

    D)  \[5W\]

    Correct Answer: C

    Solution :

                    Voltage amplitude\[{{V}_{0}}=100\,V,\]current amplitude \[{{I}_{0}}=100\,mA=100\times {{10}^{-3}}A\] Phase difference \[\phi =\frac{\pi }{3}=60{}^\circ \] Power dissipated \[p=\frac{{{V}_{0}}{{I}_{0}}}{2}\cos \phi \] \[=\frac{100\times 100\times {{10}^{-3}}}{2}\times \cos 60{}^\circ \] \[=2.5\,W\]


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