# Objectives:

• You need to be able to select and use the equation $\Delta Q = I \Delta t$;
• Define the coulomb;
• Describe how an ammeter may be used to measure the current in a circuit;
• Recall and use the elementary charge   $e = 1.6 \times 10^{-19} C$
(You will be expected to know that an electron has charge −e and a proton a charge +e)
• You need to understand and use the fact that a net charge on a particle or an object is quantised and a multiple of  $e$.

# What is electric current?

An electric charge is a physical property of matter, both electrons and protons have a charge of $-e$ and $+e$ respectively.  The charge that an electron has is $-1.6 \times 10^{-19}$  Coulombs, a proton has the same charge but is positive, $+1.6 \times 10^{-19}$  Coulombs (we will study the reason the two particles have an equal but opposite charge momentarily in year 13). As you can see from the magnitude, the charge of an electron is extremely small, and therefore is extremely difficult to measure in any experimental situation.

Electrons are the particles that flow throughout a circuit, the flow of electrons is also known as a current, the more electrons that flow in a given unit of time, the greater the current (and vice versa). If the electrons are stationary there is no current as they would take an infinitesimal amount of time to travel anywhere, therefore an electrical current is linked to time, the more electrons that flow in a given amount of time the more current there is. It is the charge that an electron has that gives the flow of electrons a current. We can link the three quantities Q, I and t together to form the equation;

$\Delta Q = I \Delta t$

where;
is the charge measured in Coulombs, C
I
is the current measured in Amperes or Amps, A
t
is the time measured in seconds, s

You will frequently come across this equation in the format $Q = I t$, whilst this can be used for most problems that you will address in year 12, the Δ’s used represent quite an important factor, to understand this in more detail it is best to rearrange the equation for current, I;

$I = \frac{\Delta Q}{\Delta t}$

Here you can see that current is equal to the amount of charge in a certain time frame. Current, as you know is the flow of electrons, well it is actually defined as the number of electrons that pass a point in one second. By its definition we know that a current cannot flow if the electrons are stationary (as mentioned above), this means that any number of electrons would take an infinite amount of time to pass a point in a given second, if we substitute this into the equation we can see that the current is zero and thus works;

$I = \frac{\Delta Q}{\infty} = 0 A$

The Delta, Δ signs will appear frequently in Physics and represents the change in value of the quantity, so $\Delta Q$ represents $Q_1-Q_2$ where $Q_1$ is the charge at one point in time and $Q_2$ is the charge at a second point in time. Whilst this is not overly important or helpful when answering questions in AS physics, it become crucial in some aspect of A2 work.

1 Coulomb is defined as the charge transported by a constant current of 1 Ampere in one second;

$1 C = 1A \times 1s$

Here are some questions for you to practice the use of the equation above with – Q=It questions.

How many electrons are there in 1 Coulomb of charge?

The charge of an electrons, also known as the elementary charge is  $e = 1.6 \times 10^{-19} C$. It can be seen that a number, n, of these charges combined is equal to 1 Coulomb, so we can write;
$1 C = n \times 1e$

We can therefore use this to determine how many electrons make up 1 Coulomb of charge, as shown;

Rearranging the above for n;

$n = \frac{1}{e}$

$n = \frac{1}{1.6 \times 10^{-19} }$

$n = 6.25\times 10^{18}$

From this equation we can see that 1 Coulomb of charge is made up of a huge number of electrons!

How doe we measure current?

In any circuit, the current that flows through the wires or components can be measured using an ammeter, which needs to be placed in series to circuit components as shown;

In simple terms, an ammeter works using the equation $I = \frac{\Delta Q}{\Delta t}$ to measure the number of coulombs of charge flowing through the ammeter per second.

Measuring 1 electron would need an extraordinary amount of precision (it is possible but not in a standard classroom laboratory), but measuring $6.25\times 10^{18}$ electrons is much more realistic.

Standard classroom ammeters may measure the current to 0.01A, however some digital multimeters (devices that can be used to measure a variety of quantities)  have the ability to measure up to 1μA ($1\times 10^{-6}$ A.

More questions using $\Delta Q = I \Delta t$link.