## Main Difference – RMS vs. Peak

In alternating currents, the magnitude of current is always changing. Therefore, the current can be described by not just one, but several numbers. RMS and peak are two numbers that can be used to express an alternating current. The **main difference** between RMS and Peak is that **peak refers to the maximum value that the current can reach **in an alternating current whereas **RMS is the peak current divided by the square root of two**.

## What is Peak

Alternating currents change sinusoidally with time. **Peak** refers to the maximum value that the sinusoidally-varying current or voltage reaches. If the voltage is expressed in the form , then the peak voltage is .

**Peak-to-peak** refers to the absolute value of the difference between maximum and minimum voltages. Peak-to-peak voltages are sometimes used to describe alternating currents. If the wave is sinusoidal, then .

## What is RMS

RMS stands for **Root Mean Square**. Root mean squares are used to express averages of a quantity when the quantity can take negative and positive values. This is necessary so that negative values of a quantity do not cancel any positive quantities. Root mean squares are used in thermodynamics; for examples, to express the average velocity of gas molecules.

Since the voltage in an AC current varies sinusoidally, if we are to take the *average* voltage, we would get an answer of zero:

Instead, we square the current. Now, the average of the *squared* current is not 0, but a half:

Suppose a voltage is expressed as

Suppose we want to find the average value of . As we discussed earlier, one approach would be to first square the voltage. We do this now to both sides of the equation:

Next, we take the averges from both sides of the equation. The average of is . So,

If we want to find the mean voltage, then we take the square roots:

The figure below illustrates the peak, peak-to-peak and RMS voltages in an alternating current.

RMS voltage is useful in calculating the **average power** in a circuit. The average power is given by . In terms of the RMS *current*, the average power is given by .

## Difference Between RMS and Peak

**DPeak** refers to the maximum value that the current or voltage reaches in an alternating current. **RMS** gives an average value for current or voltage.

When a voltage value for an AC current is quoted, it is usually the **RMS** value that is quoted.

**RMS** values are always smaller than **peak** values.

Image Courtesy:

“Graph of a sine wave voltage versus time (in degrees of angle) with RMS, peak, and peak-to-peak marked.” by AlanM1

(Derived from File:Sine wave 2.svg by en:User:Booyabazooka (CC0-licensed)) [CC0 1.0], via Wikimedia Commons