Q. 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
Delhi UMET/DPMTDelhi UMET/DPMT 2003Alternating Current
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 $\omega$ is angular frequency $ \left( \omega = \frac{ 2 \pi}{ T} \right)$.
Given, $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}{ 1 00 } s $
The current rises from zero to peak value in time $T/4$.
$\therefore $ T = $ \frac{ T}{ 4 } = \frac{ 1}{ 400} s $
