question_answer

In an AC circuit, the current is expressed as\[i=100\,\sin 200\,\pi t\]. In this circuit the current rises from zero to peak value in time :

A)  \[\frac{1}{400}s\]

B)  \[\frac{1}{300}s\]

C)  \[\frac{1}{100}s\]

D)  \[\frac{1}{200}s\]

Correct Answer: A

Solution :

 The simple type of alternating current is one, which varies with time simple harmonically, i.e, \[i={{i}_{0}}\sin \,\omega \,t\] ... (i) where cd is angular frequency \[\left( \omega =\frac{2\,\pi }{T} \right)\]. Given equation is \[i=100\,\sin 200\,\pi t\] ... (ii) Comparing Eqs. (i) and (ii), we get \[\omega =200\,\pi \] \[\Rightarrow \] \[\frac{2\pi }{T}=200\,\pi \] \[\Rightarrow \] \[T=\frac{2}{200}=\frac{1}{100}s\] The current rises from zero to peak value in time T/4. \[\therefore \] \[T=\frac{T}{4}=\frac{1}{400}s\]