KVPY Sample Paper KVPY Stream-SX Model Paper-5

  • question_answer
    Current in an ac circuit is given by \[i=3\,\,\sin \omega t+4\,\,\cos \omega t\] then -

    A) rms value of current is 5 A

    B) Mean value of this current in one half period will be 6/71.

    C) If voltage applied is \[V\text{ }={{V}_{m}}\sin \omega t\]  then the circuit must be containing resistance and capacitance.

    D) If voltage applied is \[V\text{ }={{V}_{m}}\sin \omega t\] the circuit may contain only resistance and inductance

    Correct Answer: A

    Solution :

    [C] \[i=3\sin \omega t+4\cos \omega t\]\[=5\left[ \frac{3}{5}\,\,\sin \,\omega t+\frac{4}{5}\,\,\cos \,\omega t \right]\]\[=5\,\,[\sin \,(\omega t+\delta )]\] \[\Rightarrow \]rms value \[=\frac{5}{\sqrt{2}}\]\[\Rightarrow \]mean value \[=\frac{\int\limits_{{{T}_{1}}}^{{{T}_{2}}}{idt}}{\int\limits_{{{T}_{1}}}^{{{T}_{2}}}{dt}}\] \[\therefore \]Initial value is not given hence the mean value will be different for various time intervals. If voltage applied is \[V={{V}_{m}}\sin \omega \] then i given by equation (1) indicated that it is ahead of V by \[\delta \]where \[0<\delta <90\] which indicates that the circuit contains R & C. Hence [c].

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