Root Mean Square (RMS) Value

In this article, we will get to know about RMS value. The full form of RMS is the root mean square. RMS value is calculated for voltage as well as current. RMS value for voltage is the effective voltage. Similarly, RMS value for current is also called an alternating current or an AC. As you can understand RMS is the root mean square and so it is calculated by the root of the mean of the square of instantaneous voltage or current. You must be thinking that it seems to be the average value. You are right but RMS is used only when the set of variables is random.

We will try to understand how we can calculate RMS value of current as well as voltage. Formulas that can help you calculate the RMS of a given question.

So let’s get started

Root Mean Square (RMS) Value

RMS value is that value of DC current which, when flowing until a fixed interval of time, gives the same amount of output as of AC. The RMS value of current is also called an alternating current. It can be precisely defined as the value of DC that converts electrical energy into another form at the same average rate of AC in a given resistance.

The voltage that we get in our house is an alternating voltage and refers to the RMS value of the current or root-mean-square value of current. Read on to understand what RMS value is, its formulae, and its importance.

Points to remember about RMS value

RMS value of current is also known as effective current or I-effective. The alternating current changes continuously with time. The mean value of AC for completing the full cycle is zero. The RMS value currently represented in sine waves can be determined by the area covered in half cycle.

The value of sin2 (wt) is needed to find the RMS value. The heating effects depend on I2R. RMS is one of the ways to calculate the average value of alternating current.

RMS value of AC formulae:

Irms=I02=0.707 I0

RMS voltage

It refers to root mean square voltage. RMS voltage is the effective value of alternating current or alternating voltage. It is measured by taking the root of the mean of the square of the instantaneous voltage. It is also known as the effective voltage.

Let’s take an example-

V1, V2, V3 are the instantaneous values of voltages.

In this case, the RMS voltage can be measured by –

Vrms=✓(V12 + V22 + V32)/3

Here, Vrms is the root mean square voltage. It is measured under the root of the sum of squares of all instantaneous voltages divided by the number of instantaneous voltages. The RMS value of an AC is equivalent to the power consumption by DC voltage. That’s why RMS is known as an effective value of alternating voltage.

Example –

Q) The RMS value of current in an AC circuit is 10A. What is the peak current?

Solution-

I = 10A

Peak current is given as –

I = ✓2I = ✓2 × 10 = 14.1A

For different values of voltages at the different instants of time V1, V2, V3, V4,…, Vn.

 Vrms = ✓ (V12 + V22 + V32 + V42+…+Vn2)/n

Vrms = (Vm/✓2)

Here V = VM sin(⍵t), which means the voltage is changing every second.

RMS current

Again, the effective current is called the RMS current. It is the same as root mean square current. RMS value is that value of DC current which, when flowing until a fixed interval of time, gives the same amount of output as of AC. The RMS value of current is also called an alternating current. There are two ways to find RMS current or Root Mean Square current.

1) For different values of current at the different instants of time I1, I2, I3, I4,…, In.

 Irms = ✓ (I12 + I22 + I32 + I42+…+In2)/n

Irms = (Im/✓2)

 Here I = Im. sin(⍵t), it means the voltage changes every second. The value of alternating current keeps on changing.