The instantaneous voltage through a device of impedence $20\Omega$ is $e=80\sin { 100\pi t }$. The effective value of the current is

Given equation, $e=80\sin { \left(100 \pi t \right) } .......(i)$

Standard equation of instantaneous voltage given by $E={e}_{m}\sin { \left( \omega t \right) } ..........(ii)$

Compare $(i)$ and $(ii)$, we get ${e}_{m}=80V$

where ${e}_{m}$ is the voltage amplitude.

Current amplitude ${I}_{m}=\cfrac{{e}_{m}}{Z}$ where $Z=$ impedence

$=\dfrac{80}{20}=4A$

${ I }_{ r.m.s }=\cfrac { 4 }{ \sqrt { 2 } } =\cfrac { 4\sqrt { 2 } }{ 2 } =2\sqrt { 2 } =2.828A$