Electric potential difference is the amount of energy needed to move an electric charge from one point to another. You probably know it by its more common name: voltage. It’s measured in volts (V), and it’s the fundamental “push” that drives electric current through every circuit, from the wiring in your walls to the battery in your phone.
How Potential Difference Works
Think of electric potential difference like water pressure in a pipe. A pump takes in water at low pressure, does work on it, and pushes it out at high pressure. That pressure difference is what keeps water flowing through the system. A battery does the same thing with electric charge: it takes in charge at low voltage, adds energy to it, and pushes it out at high voltage. The difference in voltage between the two ends is what drives current through a circuit.
More precisely, electric potential difference is the energy transferred per unit of charge. One volt means that one joule of energy is used to move one coulomb of charge between two points. If you double the voltage, you double the energy available to push that charge along.
The Key Formula
The basic relationship is straightforward:
ΔV = ΔU / q
Here, ΔV is the potential difference (voltage) between two points, ΔU is the change in electrical potential energy, and q is the charge being moved. You can rearrange this to find the energy: ΔU = q × ΔV. So if you know the voltage and the charge, you can calculate exactly how much energy was transferred.
This formula reveals something important: voltage is not the same as energy. Voltage is energy per unit charge. A 9-volt battery doesn’t contain 9 joules of energy. It provides 9 joules for every coulomb of charge that passes through it.
Potential vs. Potential Difference
There’s a subtle but useful distinction between electric potential and electric potential difference. Electric potential at a single point is the potential energy per unit charge at that location. Potential difference is the change in that value between two points, calculated as V_B minus V_A.
In practice, only the difference matters. The actual potential at any single point is arbitrary, because you get to choose where “zero” is. This is similar to how altitude works: you can measure height relative to sea level, relative to the ground floor, or relative to any point you like. What matters physically is the difference in height between two locations, not the absolute number. The same is true for voltage. That’s why the term “potential difference” is more descriptive than just “potential,” since it makes clear you’re comparing two points.
Voltage, Current, and Resistance
In a circuit, potential difference is the driving force behind electric current. The relationship between them is captured by Ohm’s Law:
ΔV = I × R
The potential difference across a circuit (ΔV) equals the current (I) multiplied by the resistance (R). Rearranging gives you I = ΔV / R, which tells you two things clearly: current increases when you raise the voltage, and current decreases when you increase the resistance.
This is why a higher-voltage battery pushes more current through the same device. It’s also why adding resistance (a longer wire, a smaller opening, a dimmer switch) reduces the flow. Charge flows at the greatest rate when voltage is high and resistance is low.
How Voltage Relates to Electric Fields
Potential difference and electric fields are two ways of describing the same underlying physics. An electric field points from regions of high potential to regions of low potential, and the strength of that field depends on how quickly the voltage changes over distance. In the simplest case, two parallel charged plates with a uniform field between them, the voltage drops steadily and evenly from one plate to the other. A steeper drop in voltage over a shorter distance means a stronger electric field.
This is why a spark jumps more easily across a small gap than a large one. The same voltage across a shorter distance creates a more intense field, strong enough to ionize the air and let current flow through it.
Everyday Voltage Levels
You encounter a wide range of potential differences in daily life, and the numbers give you a sense of how much energy is being delivered:
- AA battery: 1.5 V for standard alkaline cells, 1.2 V for rechargeable nickel-metal hydride versions
- USB port: 5 V for standard connections
- Car battery: 12 V
- U.S. household outlets: 120 V for standard outlets, 240 V for large appliances like dryers and ovens
- Power transmission lines: hundreds of thousands of volts, stepped down through transformers before reaching your home
The reason household voltage is so much higher than a battery’s is efficiency. Pushing current through long wires wastes energy as heat, and higher voltages allow the same power to be delivered with less current, which means less waste. That’s also why the voltage in power lines is enormous compared to what reaches your wall socket: transformers reduce it in stages as it gets closer to your home.
Why It Matters
Understanding potential difference helps you make sense of how electrical devices work and why they need specific power sources. A device rated for 120 V won’t function properly on a 12 V supply because there isn’t enough energy per charge to drive the necessary current. Plug a 120 V device into a 240 V outlet, and the doubled voltage forces too much current through the circuit, potentially destroying the device or creating a fire hazard.
Batteries wired in series add their voltages together, which is why putting four 1.5 V AA batteries end to end gives you 6 V. Each battery lifts the charge’s potential a little higher, and the total potential difference across the whole chain is the sum. This is the same principle behind every power supply that stacks cells to reach a target voltage.