• # 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

[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].