An electric current has both DC and AC compon | vedclass

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(B) The resultant current is given by $I = 8 + 6 \sin \omega t$.To find the $rms$ value,we first calculate the mean square value $\langle I^2 \rangle$

Vedclass · Accepted Answer

$9.05$

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(B) The resultant current is given by $I = 8 + 6 \sin \omega t$.To find the $rms$ value,we first calculate the mean square value $\langle I^2 \rangle$.$\langle I^2 \rangle = \langle (8 + 6 \sin \omega t)^2 \rangle$$\langle I^2 \rangle = \langle 64 + 96 \sin \omega t + 36 \sin^2 \omega t \rangle$Using the properties of average values over a full cycle: $\langle \sin \omega t \rangle = 0$ and $\langle \sin^2 \omega t \rangle = \frac{1}{2}$.$\langle I^2 \rangle = 64 + 96(0) + 36(\frac{1}{2})$$\langle I^2 \rangle = 64 + 18 = 82 \ A^2$$I_{rms} = \sqrt{\langle I^2 \rangle} = \sqrt{82} \approx 9.05 \ A$.

An electric current has both $DC$ and $AC$ components. The $DC$ component is $8 \ A$ and the $AC$ component is given as $I = 6 \sin \omega t$. The $rms$ value of the resultant current is . . . . . . (in $A$)

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