What is voltage?

Voltage is also called potential difference, because it is always a difference between two points. Our guide to potential difference covers the GCSE and A-level definitions and exam questions. A battery has a voltage between its two terminals. A single wire on its own doesn't "have" a voltage, any more than a single point on a hill has a height difference. You need two points to compare.

Voltage definition and formula

Physicists define voltage as energy transferred per unit charge:

A coulomb is the unit of charge, about 6.24 × 10¹⁸ electrons' worth. So when a 9 V battery pushes charge through a bulb, each coulomb carries 9 J of energy from the battery and hands it to the bulb, which turns it into light and heat. The SI Brochure defines the volt as one watt per ampere, which is the same as one joule per coulomb.

The volt is named after Alessandro Volta, the Italian physicist who built the first battery, the voltaic pile, in 1800 from stacked discs of zinc, copper and brine-soaked card.

How voltage works: the water analogy

Electric circuits behave a lot like water in pipes, and the comparison helps.

A higher voltage is like a stronger pump: it pushes more current through the same pipe. A higher resistance is like a narrower pipe: less flows for the same push. The analogy has limits. Charge doesn't leak out of an open switch the way water would from a cut pipe, but for most circuits it gives the right answer.

A second picture is height. Charge going through a battery is like a ball being carried up a hill: it gains energy. Going through a bulb or a motor is like rolling back down, giving that energy away. Voltage is the height of the hill.

Voltage vs current: volts vs amps

These two get mixed up more than anything else in electricity.

• Voltage (volts) is the energy per coulomb: how hard each bit of charge is pushed.
• Current (amps) is the rate of flow: how many coulombs pass a point each second. One amp is one coulomb per second.
• Power (watts) combines them: energy per second. Power = voltage × current, P = IV.

Voltage can exist without current. A battery sitting in a drawer has 1.5 V across its terminals, but no current flows until you complete a circuit. Current, on the other hand, needs a voltage to drive it.

Ohm's law: how voltage drives current

For many components, such as a resistor at a steady temperature, the current is proportional to the voltage. This is Ohm's law:

Here x is the voltage in volts and y is the current in milliamps. The line is straight through the origin: double the voltage and the current doubles. The steepness depends on the resistance, and a bigger resistance gives a shallower line.

Everyday voltages

The US uses 120 V at 60 Hz and the UK 230 V at 50 Hz, according to the US International Trade Administration. The National Weather Service puts a typical lightning flash at about 300 million volts and 30,000 amps.

Why power lines use such high voltages

Power stations are often far from homes. For a given power, P = IV, so a higher voltage means a smaller current. Cables waste energy as heat in proportion to the current squared, so stepping the voltage up to hundreds of thousands of volts cuts the losses enormously. Transformers then step it back down to a safe level before it reaches your home. National Grid runs Britain's main lines at 400,000 V and 275,000 V.

AC and DC voltage

A battery gives a direct current (DC) voltage: it pushes one way and stays steady. Mains electricity is alternating current (AC): the voltage swings from positive to negative and back, 60 times a second in the US and 50 times a second in the UK.

Because AC keeps changing, the 120 V or 230 V on the label is an average-like value called the root mean square (RMS) voltage, which delivers the same power as that DC voltage would. The voltage actually peaks higher: 120 × √2 = about 170 V in the US, and 230 × √2 = about 325 V in the UK. That is one more reason mains electricity is dangerous. Chargers and power adapters turn mains AC into the low DC voltage that phones and laptops need.

Voltage in series and parallel circuits

• Cells in series add up. Two 1.5 V batteries end to end give 3.0 V, which is why a torch (flashlight in the US) holds them in a line.
• In a series circuit, the voltage is shared. The voltages across each component add up to the supply voltage. Two identical bulbs on a 12 V supply get 6 V each.
• In a parallel circuit, every branch gets the full voltage. That is how homes are wired: every appliance gets the full 120 V or 230 V, and switching one off doesn't affect the others.

You can build both kinds of circuit and watch the voltages change in the Circuit Builder.

How to measure voltage

Voltage is measured with a voltmeter, or a multimeter set to volts. Because voltage is a difference between two points, the meter connects across a component, one lead on each side, in parallel with it. Set it to DC volts (often marked V with a straight line) for batteries, and AC volts (V with a wavy line) for mains, which should only be measured by someone trained to do so.

A voltmeter has a very high resistance, so almost no current goes through it and it doesn't change the circuit it measures. An ammeter is the opposite: it goes in series, in the loop, with a very low resistance.

Worked examples

Example 1: energy from voltage

A 9 V battery moves 2 C of charge through a bulb. How much energy does the bulb receive? Rearrange V = E ÷ Q to E = QV, so E = 2 × 9 = 18 J.

Example 2: power from voltage and current

A phone charger supplies 5 V at 2 A. What is its power? P = IV = 2 × 5 = 10 W: 10 joules every second.

Example 3: the same power at two voltages

A 3,000 W kettle in the UK runs on 230 V, and a 1,500 W kettle in the US runs on 120 V. What current does each draw? I = P ÷ V, so the UK kettle draws 3,000 ÷ 230 = 13.0 A and the US one 1,500 ÷ 120 = 12.5 A. The currents are similar, but the higher voltage lets the UK kettle deliver twice the power, which is why it boils water faster.

Example 4: Ohm's law

A current of 0.02 A flows through a 220 Ω resistor. What is the voltage across it? V = IR = 0.02 × 220 = 4.4 V.

Now try a question with charge, current and energy. Answer here, then press Mark to check it in our Electricity course.

Is voltage dangerous?

It is the current through your body that does the harm, but voltage decides whether a harmful current can flow. Dry skin has a high resistance, so a 1.5 V or 12 V battery can't push a dangerous current through you. Mains voltage can, which is why sockets, plugs and fuses are designed to keep you away from live parts. Very high voltages, like those on power lines, can even jump through the air, so stay well clear of fallen or overhead lines.

Common mistakes

• Saying current flows "through" a voltage. Voltage is across two points. Current flows through a component.
• Thinking high voltage always means high current. Current also depends on resistance: I = V ÷ R.
• Connecting a voltmeter in series. It goes in parallel, across the part you are measuring.
• Expecting each series bulb to get the full voltage. In series the supply voltage is shared. Only parallel branches each get the full voltage.
• Mixing up the volt (unit) and voltage (quantity). Voltage is what you measure, and volts are the unit, just as length is measured in metres.

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