TL;DR:
Voltage, or potential difference, is the energy given to each coulomb of charge that moves between two points:
V = W / q.One volt is one joule per coulomb. Voltage is always between two points, never at one point alone.
The water pressure analogy helps, but it breaks in a few places that matter.
A 9 V battery and a 1.5 V cell can both sit in your hand without hurting you, yet a mains outlet can be deadly. The word voltage shows up in every case, and most people could not say what it measures. Here is the plain answer.
Energy per charge, not a thing that flows
Charges feel a force in an electric field, so moving a charge from one place to another changes its energy. Voltage is that energy change for each unit of charge: V = W / q, where W is energy in joules and q is charge in coulombs.
The unit follows directly: 1 volt = 1 joule per coulomb. It is also called potential difference, because it compares the electric potential at two points. A voltage is a difference between two places, so it makes no sense to say the voltage at one point of a wire without naming what you compare it to.
A common slip is to say voltage flows. What flows is current, the rate of charge movement, measured in amps (coulombs per second). Voltage is what pushes charge along, in the sense of the energy each coulomb gets.
Why a battery has a voltage
Inside a battery, a chemical reaction pushes charge from one terminal to the other, which stores energy in that separation. A 9 V battery is built so that each coulomb that goes around the outside circuit gets 9 joules from the battery and gives those 9 joules up in the components.
That energy bookkeeping is the heart of circuit analysis. Add up the voltage gains around a loop and they equal the voltage drops. It is just energy conservation, written per coulomb.
Worked example: the water pressure analogy, and where it breaks
Picture a closed loop of pipe, filled with water, with a pump and a narrow section. Match each part to a circuit idea.
Water loop | Circuit |
|---|---|
Pump | Battery |
Pressure difference across the pump | Voltage (potential difference) |
Flow rate, litres per second | Current, coulombs per second |
Narrow pipe | Resistor |
Pipe full of water everywhere | Wire full of charge carriers everywhere |
Now put numbers on the electrical side. Say a 12 V battery pushes 5 C of charge around a circuit. The energy transferred is W = qV = 5 × 12 = 60 J. If that takes 10 s, the current is 5 / 10 = 0.5 A and the power is 60 / 10 = 6 W. Check with P = IV = 0.5 × 12 = 6 W. Both routes agree.
Where does the analogy help? A bigger pressure difference means a faster flow through the same pipe, just as a bigger voltage means more current through the same resistor. A narrower pipe means less flow, just like a larger resistance.
Where does it break? Three places matter.
Nothing is stored in a tank. The wire is already full of charge carriers. The battery does not supply the charges, it supplies the push, and the same charges circulate.
Voltage needs two points. Pressure can be quoted at one point against the atmosphere. In circuits we always compare two points, and the choice of the zero point is a convention.
The carriers drift slowly. The signal travels quickly through the wire, but the charges themselves creep along. A light comes on at once because the whole wire is already full of charge.
Voltage across a component
The voltage across a resistor is the energy each coulomb loses passing through it, found from V = IR. A 100 Ω resistor carrying 0.03 A has 0.03 × 100 = 3 V across it, so every coulomb that goes through gives up 3 J as heat.
This is why a high voltage on its own does not mean danger. What hurts is the current that passes through a body, and how much flows depends on both the voltage and the resistance in the way. Higher voltages can push more current through skin, which is why mains is treated with such care.
Measuring with a multimeter safely
A voltmeter is connected in parallel across the component, because it measures the difference between two points. A good meter has a very high resistance, so it draws almost no current.
Set the dial: Choose DC volts for a battery (a straight line with dashes on the dial). Pick a range above the voltage you expect.
Plug in the leads: Black lead into COM and red lead into the socket marked for volts. Do not use the amps socket for voltage.
Touch the probes across the part: Hold the probes by the insulated handles, red on the more positive side. A reversed reading just shows a minus sign.
Read, then disconnect: Remove the probes before changing the dial.
Low voltage only: Practise on batteries and low-voltage circuits only. Do not measure wall outlets or anything plugged into the mains unless you are trained and the meter is rated for it. Never put the probes in amps mode across a battery or outlet, which can cause a short circuit.
How to check your answer
Units. Joules per coulomb is volts. Amps times volts is watts.
Round trip. Go from
W = qVto a current and a power and confirmP = IVgives the same number.Loop test. The voltage gains around a loop must equal the voltage drops.
Where you will use it next
Voltage sets the rules for series and parallel circuits, and it connects to the picture of forces at a distance in electric and magnetic fields in plain words.
Frequently asked questions
Is voltage the same as potential difference?
Yes in circuits. Both mean the energy per charge between two points. Textbooks often say voltage for short.
Can a bird sit on a bare power line safely?
Its feet touch the same wire, so there is almost no voltage between them and almost no current through the bird. The danger comes from touching two points at different potentials. Never copy this yourself.
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