Potential Difference (Leaving Cert Physics): Revision Notes
Potential Difference
What is potential difference?
Potential difference is a fundamental concept in electricity that helps us understand how electric charges behave when they move through electric fields. Think of it as the "electrical pressure" that pushes charges from one point to another.
To truly understand potential difference, we first need to grasp the idea of potential energy in different types of fields.
Understanding potential difference is crucial for all electrical circuit analysis. It's what makes electric current flow through conductors and powers all our electrical devices.
Potential energy in different fields
Gravitational field
Imagine throwing a ball upwards near the Earth's surface. As the ball rises, it slows down, losing kinetic energy while gaining gravitational potential energy. When it falls back down, this process reverses - the ball speeds up as gravitational potential energy converts back to kinetic energy.
Electric field
Something very similar happens with charged particles in electric fields. When a charged particle moves in an electric field, its energy changes between electrical potential energy and kinetic energy, just like the ball in the gravitational field.
The key difference is that electric fields can both attract and repel charges (depending on whether they're positive or negative), whilst gravity only attracts.
Defining potential difference
The potential difference (symbol: V) between two points in an electric field is defined as:
The work done in bringing a charge of +1 coulomb from one point to another
This leads us to the fundamental formula:
Where:
- V = potential difference (volts)
- W = work done (joules)
- q = charge (coulombs)
Units and measurement
The SI unit of potential difference is the volt (V), named after Alessandro Volta, the Italian physicist who invented the electric battery.
1 volt = 1 joule per coulomb (1 V = 1 J C⁻¹)
This means that if 1 joule of work is done in moving 1 coulomb of charge between two points, then the potential difference between those points is 1 volt.
Measuring potential difference
Potential difference can be measured using a voltmeter. The voltmeter is connected across the two points where you want to measure the potential difference. The size of the reading indicates how much work would be done per coulomb of charge moved between those points.
Always remember that voltmeters measure the potential difference across components, not through them. This is different from ammeters, which measure current flowing through components.
How electric fields do work
When electric charges move in electric fields, work is either done by the field or against the field:
- Work done by the field: When a positive charge moves in the direction of the electric field, the field does work on the charge, increasing its kinetic energy
- Work done against the field: When a positive charge moves against the direction of the electric field, work must be done against the field to move the charge
The relationship between work done and potential difference is:
This equation can be rearranged to solve for any of the three variables, making it extremely useful for calculations. You can find V = W/q, W = qV, or q = W/V depending on what you need to calculate.
Relationship with electric field strength
There's an important relationship between potential difference and electric field strength. If two points A and B are a fixed distance apart, and the electric field strength between them increases, then more work must be done to move a charge from A to B. This means the potential difference between the points also increases.
The stronger the electric field, the greater the potential difference across a given distance.
Potential at a point
Sometimes it's useful to talk about the potential at a single point rather than the potential difference between two points. By convention, scientists use the Earth as a reference point with zero potential. The potential at any other point is then the potential difference between that point and the Earth.
Conductors and potential
All points on a conductor carrying static charge are at the same potential
This happens because if there were any potential difference between different points on the conductor, charges would move until they reached equilibrium. Since we're dealing with static (non-moving) charges, there can be no potential difference across the conductor.
Worked examples
Let's look at some typical calculations you might encounter:
Worked Example 1: Basic potential difference calculation
Question: The potential difference between two points is 12 V. Find the work done in transferring a charge of 8 C between the two points.
Solution: Using V = W/q, we can rearrange to get W = qV W = 8 × 12 = 96 J
Worked Example 2: Finding potential difference
Question: The work done in bringing a charge of 4 C from one point to another is 10 J. What is the potential difference between the two points?
Solution: V = W/q = 10/4 = 2.5 V
Worked Example 3: Electron movement
Question: An electron (charge 1.6 × 10⁻¹⁹ C) moves through a potential difference of 200 V. Find the speed when it arrives at the second point.
Solution: Step 1: Calculate the work done on the electron W = qV = (1.6 × 10⁻¹⁹)(200) = 3.2 × 10⁻¹⁷ J
Step 2: This work done equals the kinetic energy gained Using kinetic energy: KE = ½mv² 3.2 × 10⁻¹⁷ = ½(9.1 × 10⁻³¹)v²
Step 3: Solve for velocity v = 2.7 × 10⁶ m s⁻¹
Electric current connection
When charges flow continuously through a conductor (like a wire), we get an electric current. Current is simply a flow of electric charge, and potential difference is what drives this flow. Think of potential difference as the "electrical pressure" that pushes current through circuits.
Key Points to Remember:
- Potential difference (V) is the work done per unit charge: V = W/q
- The volt is the unit of potential difference: 1 V = 1 J C⁻¹
- Work and energy are interchangeable - work done by/against electric fields changes the potential energy of charges
- All points on a static conductor are at the same potential
- Voltmeters measure potential difference across two points in a circuit