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Q.
Alternating current in circuit is given by $I=I_0\, \sin\,2\pi\,nt$ .Then the time taken by the current to rise from zero to r.m.s. value is equal to.
Alternating Current
Solution:
Alternating current is given as $i = i _{0} \sin (2 \pi nt )$
Rms value of current $i _{ rms }=\frac{ i _{ o }}{\sqrt{2}}$
Let time taken to reach zero to r.m.s value be t.
$\therefore \frac{ i _{0}}{\sqrt{2}}= i _{0} \sin (2 \pi nt )$
Or $\sin \frac{\pi}{4}=\sin (2 \pi n t)$
Or $\frac{\pi}{4}=2 \pi n t$
$\Rightarrow t =\frac{1}{8 n }$