Question
The voltage of an $$ac$$ supply varies with time $$\left( t \right)$$ as $$V = 120\sin 100\pi \,t\cos 100\,\pi t.$$ The maximum voltage and frequency respectively are
A.
$$120\,volts,100\,Hz$$
B.
$$\frac{{120}}{{\sqrt 2 }}volts,100\,Hz$$
C.
$$60\,volts,200\,Hz$$
D.
$$60\,volts,100\,Hz$$
Answer :
$$60\,volts,100\,Hz$$
Solution :
$$\eqalign{
& {\text{Given,}}\,\,V = 120\sin \left( {100\pi t} \right)\cos \left( {100\pi t} \right) \cr
& = 60\left[ {2\sin \left( {100\pi t} \right) \cdot \cos \left( {100\pi t} \right)} \right] = 60\sin 200\,\pi t. \cr
& {\text{Thus,}}\,{V_0} = 60\,V,\omega = 200\,\pi \,\,{\text{or}}\,\,f = \frac{{200\pi }}{{2\pi }} = 100\,Hz. \cr} $$