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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