The instantaneous voltage through a device of impedence 20 is e=8… - Vidyadip

Question

The instantaneous voltage through a device of impedence $20\Omega$ is $\text{e}=80\sin100\pi\text{t}.$ The effective value of the current is.

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Answer

Given equation, $\text{e}=80\sin100\pi\text{t}.(\text{i})$
Standard equation of instantaneous voltage given by $E = \text{e}_\text{m}\sin(\omega\text{t})......(\text{i})$
Compare $(i)$ and $(ii),$ we get $e_m = 80V$
where $e_m$ is the voltage amplitude.
Current amplitude $\text{I}_\text{m}=\frac{\text{e}_\text{m}}{\text{Z}}$ where $Z =$ impedence
$=\frac{80}{20}=4\text{A}$
$\text{I}_\text{r.m.s}=\frac{4}{\sqrt{2}}=\frac{4\sqrt{2}}{2}=2\sqrt{2}=2.828\text{A}$

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