Find the effective value of current i = | vedclass

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Question

Analytically

$\mathrm{i}=2 \sin 100 \pi \mathrm{t}+2 \cos \left(100 \pi \mathrm{t}+30^{\circ}\right)$

$\Rightarrow \mathrm{i}=2 \sin 100 \pi \ma

Vedclass · Accepted Answer

$\sqrt 2\,A$

Vedclass · Answer

Analytically

$\mathrm{i}=2 \sin 100 \pi \mathrm{t}+2 \cos \left(100 \pi \mathrm{t}+30^{\circ}\right)$

$\Rightarrow \mathrm{i}=2 \sin 100 \pi \mathrm{t}+2 \cos 100 \pi \mathrm{tcos} 30^{\circ}$

$-2 \sin 100 \pi \operatorname{tsin} 30^{\circ}$

$\Rightarrow \mathrm{i}=\sin 100 \pi \mathrm{t}+\sqrt{3} \cos 100 \pi \mathrm{t}$

$\Rightarrow \mathrm{i}=\mathrm{I}_{\mathrm{m}} \sin (100 \pi \mathrm{t}+\phi)$

Where $I_{\operatorname{m}}=\sqrt{1+(\sqrt{3})^{2}}=2 A$

$I_{\operatorname{rms}}=\frac{I_{m}}{\sqrt{2}}=\frac{2}{\sqrt{2}}=\sqrt{2} A$

Find the effective value of current $i = 2\, sin\, 100\pi t + 2cos\,(100\pi t + 30^o)$

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