If a direct current of 'a' amp is sup | vedclass

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Question

$\mathrm{I}_{\mathrm{rms}}^{2}=\frac{1}{\mathrm{T}} \int_{0}^{\mathrm{T}}(\mathrm{a}+\mathrm{b} \sin \omega \mathrm{t})^{2} \mathrm{dt}$

$=\frac{1}

Vedclass · Accepted Answer

${\left[ {{a^2} + \frac{1}{2}{b^2}} \right]^{1/2}}$

Vedclass · Answer

$\mathrm{I}_{\mathrm{rms}}^{2}=\frac{1}{\mathrm{T}} \int_{0}^{\mathrm{T}}(\mathrm{a}+\mathrm{b} \sin \omega \mathrm{t})^{2} \mathrm{dt}$

$=\frac{1}{\mathrm{T}} \int_{0}^{\mathrm{T}}\left(\mathrm{a}^{2}+\mathrm{b}^{2} \sin ^{2} \omega \mathrm{t}+2 \mathrm{ab} \sin \omega \mathrm{t}ight) \mathrm{d} \mathrm{t}$

$=\frac{1}{\mathrm{T}}\left(\mathrm{a}^{2} \mathrm{T}+\frac{\mathrm{b}^{2}}{2} \mathrm{T}+0ight)=\mathrm{a}^{2}+\frac{\mathrm{b}^{2}}{2}$

$	herefore \,\,{I_{rms}} = \sqrt {{a^2} + \frac{{{b^2}}}{2}} $

If a direct current of $'a'$ amp is superimposed with an alternating current $'I = b\,sin \,\omega t',$ then effective value of resulting current is

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