Physics - EMI/AC Question with Solution | TestHub

Given,

$\mathrm{I}=10\sin \left(314\mathrm{t}\right) \mathrm{A}$and$\mathrm{V}=100\sin \left(314\mathrm{t}\right) \mathrm{V}$

Comparing with$\mathrm{I}={\mathrm{I}}_0\mathrm{sin\omega t}$ and$\mathrm{V}={\mathrm{V}}_0\mathrm{sin\omega t}$,we get

$\therefore {\mathrm{I}}_0=10 \text{A}$ and ${\mathrm{V}}_0=100 \text{V}$

$\begin{array}{l}\Rightarrow {\mathrm{I}}_{\text{rms}}=\frac{10}{\sqrt{2}} \text{A, }{\mathrm{V}}_{\text{rms}}=\frac{100}{\sqrt{2}} \text{V,}\\ \text{Phase difference }\mathrm{\varphi }{\text{=0}}^{\text{o}}\\ \therefore \text{\hspace{0.17em}Power\hspace{0.17em}dissipated\hspace{0.17em}}{\mathrm{P}}_{\text{av}}={\mathrm{V}}_{\text{rms}}\times {\mathrm{I}}_{\text{rms}}\times \mathrm{cos\varphi }\\ =\left(\frac{10}{\sqrt{2}}\right)\left(\frac{100}{\sqrt{2}}\right)\cos {\text{0}}^{\text{o}}\\ =500\text{\hspace{0.17em}W}\end{array}$