RMS Value or Root Mean Square Value of Voltages and Currents


The symmetrical alternating voltages and currents have a specific amplitude. But this amplitude does not directly indicate the effective value of the alternating voltages and currents. It is because a sinusoidal alternating quantity achieves its maximum value or amplitude for an instant only during every half cycle. But at all other instants,∫ the value of the alternating quantity is less than the amplitude.

Also, the symmetrical alternating quantity has an average value of zero. Therefore, there must be some quantitative representation of the alternating voltages and currents which practically indicates the effectiveness of those voltages and currents. From here the concept of RMS value or Root Mean Square value comes into the picture.

amplitude of sinusoidal voltage

Concept of RMS or Root Mean Square Value

Whenever an alternating current flows through a resistor it produces heat in the resistor. Also, a direct current produces a heating effect on the resistor. But in the case of direct current, it is quite easy to calculate the quantity of heat generated due to that direct current. The amount of heat generated by direct current is,

RMS equation 2
Where ‘I’ is the average value of the direct current.

In the case of sinusoidal alternating current, the average value is 0. Therefore, we cannot directly use that average value (0) for calculating the heating effect of an alternating current. But obviously an alternating current has a heating effect on the resistor. Let us write the expression of the heat due to alternating current as follows.

RMS equation 2
Now, I’ is a virtual value of the alternating current. This value determines the heating effect of the alternating current. The value is the RMS value or Root Mean Square Value of the alternating current.

Significance of RMS Value

By equating equation 1 and 2 we get
RMS equation 3
The above equation signifies that the direct current produces the same heating effect on the same resistor as the alternating current. Therefore we can say that I’ is the DC equivalent of the alternating current. In other words, the RMS value of an alternating current is the DC equivalent of the alternating current.

Definition of RMS Current

The RMS current is an equivalent steady direct current for alternating current. The RMS current produces the same heating effect on the same resister for the same period of time which the alternating current does.

Calculation of Root Mean Square Value

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