The root mean square (RMS) value of the alter | vedclass

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(C) The root mean square $(RMS)$ value of an alternating current is defined as the value of the steady current which,when flowing through a given resi

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$1/\sqrt{2}$ times the peak value

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(C) The root mean square $(RMS)$ value of an alternating current is defined as the value of the steady current which,when flowing through a given resistor for a given time,produces the same amount of heat as the alternating current does over the same period.Mathematically,for a sinusoidal alternating current $I = I_0 \sin(\omega t)$,the $RMS$ value $(I_{rms})$ is given by:$I_{rms} = \sqrt{\frac{1}{T} \int_{0}^{T} I^2 dt}$Solving this integral over one complete cycle yields:$I_{rms} = \frac{I_0}{\sqrt{2}}$Where $I_0$ is the peak value of the current.Therefore,the $RMS$ value is $\frac{1}{\sqrt{2}}$ times the peak value.

The root mean square $(RMS)$ value of the alternating current is equal to:

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