SI Units Explained with Worked Examples





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  Electric current

Electric current is a flow of electricity through a medium and its SI unit is the ampere with the symbol A. The flow is typically through a wire and composed of electrons, the tiny particles that make up electricity. For most practical purposes the ampere is a measure of the amount of electric charge passing a particular point in a given time. To illustrate the ampere we can ask the simple question: how many electrons does it take to make a cup of tea?

How many electrons are needed to make a cup of tea?

We more often than not refer to the ampere simply as an amp, and an amp has the units of 1 coulomb per second. Mathematically we can show this as 1 A = 1 C/s. But what is a coulomb? It is the derived SI unit of electric charge and 1 coulomb contains around 6.241 x 1018 electrons. Let's look at that number written out fully:


Remember that this is the amount of electrons passing a single point in a wire every single second. There are so many of them that it's natural to assume that they are whizzing past at some tremendous speed, but that's not the case. In fact, they are moving very slowly - typically only about a metre or two an hour, but they are very, very small.

So we know that 1 A = 1 C/s and we know how many electrons there are in a coulomb. A typical kettle will draw about 2000 watts of power, and how many coulombs per second that is depends on the voltage being used. In England, a country associated with drinking copious amounts of tea, the mains voltage is 230v so we will use that as our example. Amps can be calculated from watts divided by voltage so in England (and the rest of the UK) a 2000W kettle will use around:

2000W/230v = 8.7A

In other words around 8.7 coulombs per second. It takes about 90 seconds to boil enough water for a cup of tea, and an amp is a coulomb per second, so to boil the water in the kettle it will need:

90 s x 8.7 A = 783 coulombs

We can now finally work out how many electrons we need to make a cup of tea. The answer is simply the number of coulombs multiplied by the number of electrons in a coulomb:

783 x 6.241 x 1018 = 4.887 x 1021 electrons

Writing that out fully we get:

4,887,000,000,000,000,000,000 electrons

Why not try working out how long it would take to count that number of electrons at a rate of one electron a second? (Answer at the bottom of the page.)

In the US the mains voltage is lower at 120v. That means even more electrons are needed to boil the same amount of water. Carrying out the mathematics (as above) it takes about 16.7 amps, or about 9.380 x 1021 electrons. Note that same amount of power is used in both the UK and US examples. The difference is that the number of electrons passing a single point in the wire is greater in the UK than the US, but the energy each electron possesses is lower. We can either use a lot of low energy electrons, or many fewer electrons but each with higher energy.

Finally, note that the actual number of electrons will be a little different (by percentage) to those calculated here. For a more precise answer we would need to measure the initial temperature of the water and take electrical resistance into account, as well as a number of other factors. Still, the final answer will be close enough and certainly gives a sense of understanding electric current and its SI unit, the ampere.

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Answer to question:

A year is about 60 x 60 x 24 x 365 = 31500000 seconds.

So it would take 4887000000000000000000 divided by 31500000 = 1500000000000000 years to count the electrons at one a second, 24 hours a day, 365 days a year (you can take a day off each leap year...)

To put this into context, it would take about 1.5 x 1015 years to count the electrons. The age of the Universe is 13.7 x 1010 years, so it would take longer to count the electrons than the Universe has been around for. Best get started now...