If $\mathrm{E}=100 \sin (100 \mathrm{t})$ volt and\ $\mathrm{I}=100 \sin \left(100 \mathrm{t}+\frac

Question

If $\mathrm{E}=100 \sin (100 \mathrm{t})$ volt and\ $\mathrm{I}=100 \sin \left(100 \mathrm{t}+\frac{\pi}{3}ight) \mathrm{mA}$ are the instantaneous values of voltage and current, then the rms values of voltage and current are respectively\

Professor PC Thomas Classes · Answer

The instantaneous value of voltage is $\mathrm{E}=100 \sin (100 \mathrm{t}) \mathrm{V}$\ Compare it with $\mathrm{E}=\mathrm{E}_{0} \sin (\omega \mathrm{t}) \mathrm{V}$\ We get $\mathrm{E}_{0}=100 \mathrm{~V}, \omega=100 \mathrm{rads}^{-1}$\ The rms value of voltage is\ $\mathrm{I}=100 \sin \left(100 \mathrm{t}+\frac{\pi}{3}ight) \mathrm{mA}$\ Compare it with $\mathrm{I}=\mathrm{I}_{0} \sin (\omega \mathrm{t}+\phi)$\ We get\ $\mathrm{I}_{0}=100 \mathrm{~mA}, \omega=100 \mathrm{rads}^{-1}$\ The rms value of current is\ $\mathrm{I}_{\mathrm{rms}}=\frac{\mathrm{I}_{0}}{\sqrt{2}}=\frac{100}{\sqrt{2}} \mathrm{~mA}=70.7 \mathrm{~mA}$\