A) rms value of current is 5 A.
B) mean value of this current in one half period will be \[6/\pi .\]
C) if voltage applied is \[V={{V}_{m}}\sin \,\,\omega \,t\] at then the circuit must be containing resistance and capacitance.
D) if voltage applied is \[V={{V}_{m}}\sin \,\,\omega \,t,\] the circuit may contain only resistance and inductance.
Correct Answer: C
Solution :
| \[i=3\sin \omega \,t+4\cos \omega \,t\] |
| \[=5\,\,\left[ \frac{3}{5}\sin \omega \,t+\frac{4}{5}\cos \omega \,t \right]\] |
| \[=5\,[\sin \,(\omega \,t+\delta )]\] ?(1) |
| \[\Rightarrow \] 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 \[V={{V}_{m}}\sin \omega \,t\] then i given by equation (1) indicates 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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