The effective value of alternating current is equal to the value of the steady current (DC Current), which, when passed through a resistor for a specified time, produces the same amount of heat that an alternating current when passed through the same resistor for the same time. The effective or RMS value of alternating current is also called the RMS value.
Let us understand this definition with an example.
Suppose 15 ampere AC RMS or effective current passes through a resistor that has 10 ohms resistance. Then, the heat produced in the resistor is;
Now, if the steady current passes through the same resistor for the same time, what is the current’s magnitude that can produce the 2250 watts?
As per the definition, the 15 ampere DC current or steady current will produce the same amount of heat. Thus, if 15 ampere DC current flows through the 10 ohms resistor, it will produce the same amount of heat, i.e., 2250 watts.
The effective value or RMS value of alternating current is shown in the image below.
Methods of Calculation of RMS Value
There are two methods that can be used to calculate the RMS value.
- Graphical method
- Analytical Method
Formulas for RMS Value of Alternating Current
For the Graphical method,
RMS value = square 𝐫𝐨𝐨𝐭 of 𝐦𝐞𝐚𝐧 of the 𝐬𝐪𝐮𝐚𝐫𝐞𝐬 of the current
For analytical Method,
For Derivation of Formulas, you may read– Derivation of RMS value of AC current.
Numerical Example #1 on Effective or RMS Value of Alternating Current
A sinusoidal current has a maximum value of 10 amperes. What is its RMS value?
Solution
Numerical Example #2
The equation of alternating voltage is given by i = 400 𝑠𝑖𝑛314𝑡. Calculate RMS value
Solution
The maximum value of the current is 400 volts.
