Power Equations

Table of Contents

Introduction

In this blog post I will attempt to explain another triplet of equations that are very important to electronic theory.

These are the three equations we can use to calculate power, in Watts, when we know Voltage and current, Voltage when we know power and current, or current when we know power and voltage.

The Units of Measure

First of all we need to know about three units of measure. These are:

  • Power, in Watts, represented by the capital letter P
  • Voltage, represented by the capital letter V
  • Current, represented by the capital letter I

Power

What is power?

The power flowing in any part of a circuit is the product of the Voltage (potential) and the current.

Voltage

A unit of potential, or ‘push’ measured between two points in a circuit. The circuit may be test points on a circuit board, the terminals of a cell or a battery of cells, or even the potential between a storm cloud and the ground. But I suspect we aren’t going to get very far trying to calculate the power passing through the air from cloud to ground in a lightning strike.

Current

Current, measured in Amperes, is the rate of flow of electrons in a conductor, such as a length of copper wire.

A Triplet of Equations

Like Ohm’s Law, there are three calculations. And given 2 of the values, we can calculate the third:

  • P = V * I (power = Voltage times current)
  • V = P / I (Voltage = power over current)
  • I = P / V (current = power over voltage)

See the earlier blog post explaining Ohm’s Law for our first triplet.

From the above list of three equations it can be seen that given two of the three units of measure, it is possible to calculate the third.

There is a very simple way to remember the three equations, for which I need to describe a simple diagram.

Imagine a blank sheet of paper in front of you, upon which you have drawn a triangle, with the flat base at the bottom and the pointed apex of the triangle at the top.

Now imagine you have drawn a horizontal line across the inside of the triangle half-way down it’s height, which divides the triangle into a smaller triangle at the top and a trapezoid at the bottom.

Now write in the letters which represent the three units of measure:

  • Write a capital P in the top of the top smaller triangle, just under the apex.
  • Write a capital V inside the lower trapezoid, just inside it at what was the lower left point of the original triangle.
  • Write a capital I at the lower right corner of the trapezoid.
  • Finally, write a small x half-way between the I and the R.

You can now imagine covering any one of the three units with the tip of one finger and ‘seeing’ the equation you need to calculate it.

Cover the P at the top, and you can ‘read off’ the equation:

P = V x I (power = Voltage times current)

Cover the V, and you have:

V = P / I (Voltage = power over current)

Cover the I and you have:

I = P / V (current = power over voltage)

In the last two the line you drew to divide the original triangle represents the ‘over’, or divide line.

Simple Example

Suppose you have connected a resistor of ten Ohms across a potential (Voltage) of ten Volts.

Using our shiny new knowledge of Ohm’s Law, we can calculate the current which will flow through a ten Ohm resistor when ten Volts is connected across it:

I = V / R (current = Voltage over resistance)

Plugging in the two values we know:

I = 10 (Volts) / 10 (Ohms)

And we have known since we were about six that ten divided by ten is, erm, one.

So there is one Amp of current in the circuit.

How Big Does My Resistor Have to be?

Armed with the current in addition to the Voltage, we can calculate power:

P = 10 (Volts) x 1 (Amps)

And ten times one is ten.

There are ten Watts flowing in this simple circuit.

So the resistor needs to be of at least ten Watts power rating, or preferably more, if it is not to overheat and release the magical geeky electronic smoke.

Its a Law Jim, but not as we Know it

I have never seen this triplet of equations referred to by any name which suggests ‘law’, in the same way that the name Ohm’s Law is applied to the three equations of Voltage, current and resistance.