RAJASTHAN ­ PET Rajasthan PET Solved Paper-2009

  • question_answer
    Voltage V and current\[i\]in AC circuit are given by \[\begin{align}   & V=50\sin (50\,t)\,volt \\  & i=50\,\sin \,\left( 50t+\frac{\pi }{3} \right)mA \\ \end{align}\] The power dissipated in circuit is

    A)  5.0 W            

    B)  2.5 W

    C)  1.25 W           

    D)  zero

    Correct Answer: D

    Solution :

     Given, \[{{V}_{0}}=50\,\sin (50t)V\] Maximum voltage, \[{{V}_{0}}=50\,V\] \[i={{i}_{0}}\sin \left( 50t+\frac{\pi }{3} \right)mA\] Maximum current, \[{{i}_{0}}=50\text{ }mA=50\times {{10}^{-3}}A\] Power dissipated, \[P=\frac{{{i}_{0}}}{\sqrt{2}}\times \frac{{{V}_{0}}}{\sqrt{2}}\] \[=\frac{50\times 50\times {{10}^{-3}}}{2}\] \[=\frac{2500\times {{10}^{-3}}}{2}=1.25\,W\]


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