Peak and r.m.s values

Introduction to AC values

If you look at the back of your television or the electric fan in your parlor, you will see something like 220V or 240V written on it. This is the electricity from NEPA or PHCN. But did you know that this voltage is not steady? It is constantly going up and down in a wave pattern.

Peak voltage or current

Think of a child on a swing at the playground. The highest point the child reaches before coming back down is like the peak value. In an AC circuit, the peak value is the maximum height the electricity reaches.

It is the highest point the electricity reaches on its way up or down.

Root mean square value

If you use a generator to pump water, the generator works hard to produce a certain amount of heat or energy. The r.m.s. value is the steady 'effective' value that gives us the same heating effect as a DC battery.

It is the effective or working value that your voltmeter or ammeter actually measures.

The relationship formula

There is a simple connection between these two values. The peak value is always bigger than the r.m.s. value. To find the r.m.s. value, we divide the peak value by the square root of 2 (which is roughly 1.414).

1. I_rms = I₀ / (root 2)

2. V_rms = V₀ / (root 2)

3. I₀ = I_rms x (root 2)

4. V₀ = V_rms x (root 2)

Note that I₀ and V₀ represent the peak values while I_rms and V_rms represent the r.m.s. values.

Worked example

A small radio is connected to a 240V AC supply. Calculate the peak voltage of the supply.

1. Identify the given value: The 240V written on the supply is the r.m.s. value (V_rms = 240V).

2. Choose the formula: We need the peak voltage (V₀), so V₀ = V_rms x (root 2).

3. Substitute the numbers: V₀ = 240 x 1.414.

4. Final answer: V₀ = 339.36V.