Potential Difference and Electromotive Force (Leaving Cert Physics): Revision Notes

Potential Difference and Electromotive Force

What is potential difference?

Potential difference is a fundamental concept in electricity that describes how energy changes as electric charge moves through a circuit. When we talk about potential difference between two points in a circuit, we're measuring the energy that one coulomb of charge loses as it travels from one point to another.

The potential difference (V) between two points in a circuit represents the energy lost by one coulomb as it moves from one point to the other. This energy doesn't just disappear - it gets converted into other forms like heat, light, or mechanical energy.

Energy changes in a simple electric circuit

Understanding how energy transforms in circuits helps us grasp why potential difference matters. When electric current flows through a conductor, something important happens to the energy.

In any conductor carrying current, electrical potential energy gets converted into heat energy. This happens because the moving electric charges (usually electrons) collide with atoms in the conductor material. Each collision transfers some kinetic energy to the atoms, making them vibrate more - and that's what we experience as heat.

This is why electrical appliances like kettles, toasters, and heaters get warm when they're working - they're designed to convert electrical energy into heat energy efficiently.

Potential difference between two points in a circuit

Let's get more specific about measuring potential difference. The amount of electrical potential energy lost by one coulomb as it moves from one point to another in a circuit is called the potential difference between those two points.

Since potential difference is measured in volts, we often just call it voltage. This makes sense because both terms describe exactly the same thing - the energy change per unit charge.

The mathematical relationship is straightforward:

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

Where:

• V = potential difference (voltage) in volts
• W = work done (energy converted) in joules
• q = charge in coulombs

The rate of heat production in current-carrying conductors

Power is the rate at which work is done, and it's also the rate at which energy converts from one form to another. In electrical circuits, we're particularly interested in how quickly electrical energy converts to other forms.

Power is measured in watts (W), where 1 watt equals 1 joule per second. For electrical circuits, we can calculate power using:

$P = VI$

Where:

• P = power in watts
• V = voltage in volts
• I = current in amperes

Voltages in series and parallel circuits

Understanding how voltage behaves in different circuit configurations is crucial for analysing more complex electrical systems.

Voltages in series

In series circuits, components connect end-to-end in a single path. The key principle here comes from conservation of energy.

When components connect in series, the total voltage lost across all components equals the supply voltage. This makes perfect sense from an energy perspective - all the energy supplied must be accounted for somewhere in the circuit.

For a series circuit: $V = V_1 + V_2 + V_3$

Voltages in parallel

Parallel circuits work differently because they provide multiple paths for current to flow.

In parallel circuits, each component connects directly across the same two points. This means every component experiences the same potential difference - they all get the full supply voltage.

For parallel circuits: $V = V_1 = V_2 = V_3$

Measuring potential difference

To measure potential difference in practice, we use an instrument called a voltmeter. The key to using a voltmeter correctly is understanding how to connect it.

The voltmeter essentially measures how much energy each coulomb of charge loses as it passes through the component you're testing.

Electromotive force (emf)

To keep current flowing in a circuit, we need to maintain an electric field. This requires a potential difference between the ends of the circuit, which is provided by an electromotive force or emf.

What is emf?

Electromotive force is not actually a force - it's a voltage. The emf of a source (like a battery) represents the amount of electrical potential energy it gives to each coulomb of charge as the charge passes through the source.

Think of a battery as an energy converter:

• Chemical energy gets converted to electrical energy
• Each coulomb of charge gains energy as it passes through the battery
• This energy gain per coulomb is the emf
• The unit is the volt, just like potential difference

Battery construction

A cell typically contains two different metals separated by various chemicals in a container. Chemical reactions in the cell cause a voltage to develop between the two metals. When we say "1.5 volt AAA battery," we're describing a cell that provides 1.5 joules of energy to each coulomb of charge passing through it.

What we commonly call a "battery" is often actually several cells connected together to provide higher voltage or more energy storage.

Sources of emf connected in series

When several batteries or other sources of emf connect in series, their voltages add together, just like resistances in series circuits.

If several batteries connect in series (positive terminal of one connected to negative terminal of the next), then the total voltage equals the sum of individual voltages:

$\text{Total emf} = \text{emf}_1 + \text{emf}_2 + \text{emf}_3$

This principle explains many everyday applications:

• A torch using three 1.5V cells provides 4.5V total
• Car batteries often contain six 2V cells in series for 12V total
• Solar panels connect in series to achieve higher voltages

Key formulas summary

Here are the essential equations you need to remember:

Quantity	Formula	Units
Potential difference	$V = \frac{W}{q}$	V (volts)
Power	$P = VI$	W (watts)
Series voltages	$V = V_1 + V_2 + V_3$	V (volts)
Parallel voltages	$V = V_1 = V_2 = V_3$	V (volts)
Series emf	$\text{emf} = \text{emf}_1 + \text{emf}_2 + \text{emf}_3$	V (volts)