Basics of electricity

Welcome to the foundation of your A-Level electricity studies! You likely remember many of these concepts from GCSE, but at A-Level, we need to be much more precise with our language and definitions.

What you'll learn:

• The formal definition of electric current as the rate of flow of charge.
• How to define potential difference in terms of work done per unit charge.
• The true definition of electrical resistance (and why it isn't quite the same as Ohm's Law).
• How to set up basic circuits to measure these quantities.

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Electric Current

At its heart, electricity is all about moving charge. In metal wires, these moving charges are electrons, but in liquids (electrolytes) or gases, they could be positive or negative ions.

We measure the "amount" of charge in a unit called the Coulomb (C). However, knowing the total charge sitting in a wire isn't very useful on its own. We usually want to know how fast that charge is moving past a specific point.

This gives us our first formal definition:

We can write this mathematically as:

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

Where:

• $I$ is the current, measured in Amperes (A).
• $\Delta Q$ is the change in charge (or amount of charge flowing), measured in Coulombs (C).
• $\Delta t$ is the time interval, measured in seconds (s).

Because of this equation, we can also say that 1 Ampere is exactly equal to 1 Coulomb of charge passing a point every 1 second ($1A=1{C\; s}^{-1}$).

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Potential Difference

Current tells us that charge is moving, but why is it moving? And how much energy does it carry? This is where potential difference (often casually called voltage) comes in.

When a battery pushes electrons around a circuit, it transfers electrical energy to them. When those electrons pass through a component (like a bulb or a resistor), they transfer that energy to the component (which turns it into light or heat).

In physics, when energy is transferred, we say work is done.

The equation for potential difference is:

$$V=\frac{W}{Q}$$

Where:

• $V$ is the potential difference, measured in Volts (V).
• $W$ is the work done (or energy transferred), measured in Joules (J).
• $Q$ is the charge, measured in Coulombs (C).

This means that 1 Volt is exactly equal to 1 Joule of energy being transferred by 1 Coulomb of charge ($1V=1{J\; C}^{-1}$). If you have a 12 V car battery, it gives exactly 12 Joules of energy to every single Coulomb of charge that passes through it.

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Resistance

When charge flows through a component, it doesn't usually get a free ride. The moving electrons collide with the vibrating positive ions in the metal lattice of the wire or component. These collisions transfer energy away from the electrons (generating heat) and make it harder for the current to flow.

This opposition to the flow of current is called resistance.

Mathematically, this is written as:

$$R=\frac{V}{I}$$

Where:

• $R$ is the resistance, measured in Ohms ($\Omega$).
• $V$ is the potential difference, measured in Volts (V).
• $I$ is the current, measured in Amperes (A).

An Ohm is defined as $1{V\; A}^{-1}$. If a component has a resistance of $5\Omega$, it means it requires exactly 5 Volts of "push" to make 1 Ampere of current flow through it.

Measuring these basics in a circuit

To calculate the resistance of a component, you need to measure both $V$ and $I$. You are expected to know how to construct a standard circuit to do this.

Notice the placement of the meters:

• Ammeters measure current (flow). They must be placed in series with the component so the charge flows through them.
• Voltmeters measure potential difference (energy drop). They must be placed in parallel across the component to compare the energy of the charge before and after it passes through.

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