For a domestic AC supply of 220 ,V at 50 ,cps | vedclass

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Question

(A) For a domestic $AC$ supply,the given voltage $220 \,V$ represents the root-mean-square $(V_{	ext{rms}})$ value.The peak voltage $(V_{	ext{max}})

Vedclass · Accepted Answer

$V(t)=220 \sqrt{2} \cos 100 \pi t$

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(A) For a domestic $AC$ supply,the given voltage $220 \,V$ represents the root-mean-square $(V_{	ext{rms}})$ value.The peak voltage $(V_{	ext{max}})$ is calculated as $V_{	ext{max}} = V_{	ext{rms}} 	imes \sqrt{2} = 220 \sqrt{2} \,V$.The frequency $f$ is $50 \,cps$ (or $50 \,Hz$). The angular frequency $\omega$ is given by $\omega = 2 \pi f = 2 \pi 	imes 50 = 100 \pi \,rad/s$.The instantaneous potential difference $V(t)$ is expressed as $V(t) = V_{	ext{max}} \cos(\omega t)$.Substituting the values,we get $V(t) = 220 \sqrt{2} \cos(100 \pi t) \,V$.

For a domestic $AC$ supply of $220 \,V$ at $50 \,cps$,the potential difference between the terminals of a two-pin electric outlet in a room is (in volt) given by

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