Question

Explain the physical process on the basis of which the rms value of ac is defined

Answer 1

Explanation:

 other words (as an example), the RMS value of AC (current) is the direct current which when passed through a resistor for a given period of time would produce the same heat as that produced by alternating current when passed through the same resistor for the same time.

Answer 2

Given that,

The physical process on the basis of which the rms value of ac

Suppose, Drive the expression for r.m.s. value of an alternating voltage.

We know that,

RMS is root mean square value of the AC signal.

We need to drive the expression for r.m.s value

Using formula of rms

$\bar{i^2}=\dfrac{\int_{0}^{T}{i^2}dt}{\int_{0}^{T}{dt}}$

$\bar{i^2}=\dfrac{1}{T}\int_{0}^{T}{i_{0}^2\sin^2(\omega t+\phi)dt}$

$\bar{i^2}=\dfrac{i_{0}^2}{2T}\int_{0}^{T}{(1-\cos2(\omega t+\phi))dt}$

$\bar{i^2}=\dfrac{i_{0}^2}{2T}(t-\dfrac{\sin2(\omega t+\phi)}{2\omega})_{0}^{T}$

$\bar{i^2}=\dfrac{i_{0}^2}{2T}(T-\dfrac{\sin(4\pi+2\phi)-\sin 2\phi}{2\omega})$

$\bar{i^2}=\dfrac{i_{0}^2}{2}$

$\bar{i}=\dfrac{i_{0}}{\sqrt{2}}$

This is the rms value of current .

The r.m.s. value of voltage for alternating signal

$\bar{v}=\dfrac{v_{0}}{\sqrt{2}}$

Hence, The root mean square value of current for AC signal is $\dfrac{i_{0}}{\sqrt{2}}$