The instantaneous voltage through a device of impedance $20 \Omega$ is e $=80 \sin 100 \pi \mathrm{t

Question

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

Professor PC Thomas Classes · Answer

Given equation, $\mathrm{e}=80 \sin 100 \pi \mathrm{t}$... Standard equation of instantaneous voltage is given by\ $\mathrm{e}=\mathrm{e}_{\mathrm{m}} \sin \omega \mathrm{t}$\ Compare (i) and (ii), we get $\mathrm{e}_{\mathrm{m}}=80 \mathrm{~V}$\ Where $e_{m}$ is the voltage amplitude Current amplitude $I_{m}=\frac{e_{m}}{Z}$ where $Z=$ impedance $\mathrm{I}_{\mathrm{m}}=\frac{80}{20}=4 \mathrm{~A}$.\ Effective current or root mean square current.\ $\mathrm{I}_{\mathrm{rms}}=\frac{4}{\sqrt{2}}=\frac{4 \sqrt{2}}{2}=2 \sqrt{2}=2.828 \mathrm{~A}$\