# Mean value & RMS value of Current & Voltage

##### Mean Value of Voltage and Current :

The mean value of sinusoidal current or voltage in one complete cycle is zero, for half cycle, the mean value can be found as given below.

I = I0 sin ωt

$\displaystyle I_m = \frac{\int_{0}^{T/2}I dt}{\int_{0}^{T/2}dt}$

$\displaystyle I_m = \frac{2 I_0}{\pi}$

Similarly ,

$\displaystyle V_m = \frac{2 V_0}{\pi}$

##### Root Mean square value of voltage & current :(Vrms & Irms)

I = I0 sin ωt

$\displaystyle I_{rms} = \sqrt{\frac{\int_{0}^{T}I^2 dt}{\int_{0}^{T}dt}}$

$\displaystyle I_{rms} = \frac{I_0}{\sqrt 2}$

Similarly ,

$\displaystyle V_{rms} = \frac{V_0}{\sqrt 2}$

Exercise : The peak value of an alternating current is 10 A. Find its rms value.

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