From energy and work to electrical potential — a first-principles approach
Voltage seems abstract until you ground it in something physical: energy and work. So let's begin there.
When you lift a book off the ground, you do work. You apply a force (against gravity) over a distance, and the book gains energy. The relationship is simple:
The book doesn't care how long you take to lift it — only the force and distance matter. A fast lift and a slow lift both deliver the same amount of energy to the book.
Now imagine something slightly different: a waterfall. Water at the top has gravitational potential energy. As it falls, gravity does work on the water, converting that potential energy into kinetic energy (motion). The amount of work per unit of water depends on how high the water started — the height of the fall.
Electricity works the same way, but with electric fields instead of gravity.
A battery or power supply creates an electric field — an invisible push on charged particles. This field exerts a force on charges, just like gravity exerts a force on mass. When a charge moves through this field, the field does work on the charge.
Just like the waterfall, we care about how much work the field does per unit of charge. This is voltage:
If a battery is rated at 9 volts, it means: for every coulomb of charge that moves through the battery, the battery does 9 joules of work on that charge. The battery's electric field pushes charges uphill (in terms of energy), storing potential energy in them — just like lifting water to the top of a waterfall.
Imagine a charge moving through an electric field. Use the sliders to see how voltage and charge interact to produce energy.
What you're seeing: On the left, a battery at a certain voltage. In the middle, charges. On the right, the total energy delivered. When you increase voltage, each charge carries more energy. When you increase the number of charges, the total energy grows (but the energy per charge stays the same, since that's defined by voltage).
Voltage is also called electric potential — and the name makes sense once you think about it.
A charge sitting inside an electric field has potential energy, just like a ball at the top of a hill. If you release the charge, the field does work on it, converting that potential energy into kinetic energy (motion). The electric potential at a point is the potential energy per unit charge at that point.
This is why we talk about voltage differences. It's not the absolute potential that matters (just like it's not the absolute height that matters in gravity — only the height difference between two points). What matters is: if I move a charge from point A to point B, how much work does the field do?
Here's where voltage becomes practically useful. A battery creates a voltage — a potential difference between its two terminals. This means:
When you connect a wire between the terminals, charges flow through the wire, and the electric field inside the wire does work on them. This flowing charge is current. The voltage doesn't determine the current directly — that depends on resistance. But voltage tells you how much energy each charge will gain or lose.
Now we connect voltage to something even more practical: power — energy per unit time.
If a battery delivers voltage V, and current I flows through it, then the power it delivers is:
Why does this make sense? Current I is the charge flowing per second (coulombs per second). Voltage V is the energy per charge (joules per coulomb). Multiply them together:
So a 12-volt battery delivering 5 amps of current supplies 60 watts of power — meaning 60 joules of energy per second being transferred to whatever is connected.
See how power changes when you adjust voltage and current. The relationship is direct and linear.
In a circuit, voltage appears across components — resistors, LEDs, motors, speakers. When current flows through a component, the component's voltage tells you how much energy per charge is being dissipated (or converted).
By Ohm's law, the voltage across a resistor is:
A 1-amp current through a 10-ohm resistor produces a 10-volt drop. This voltage drop represents energy being converted into heat (the resistor gets warm). The power dissipated is:
In a circuit, voltages add up. If a 12-volt battery is connected to three resistors in series, the voltage drops across all three must sum to 12 volts (this is Kirchhoff's Voltage Law). The battery pushes charges uphill by 12 volts total, and the three resistors pull them downhill by a combined 12 volts.
Energy per unit charge. Measured in volts (V).
Formula: V = W / Q
It represents the potential energy stored at a point in an electric field.
Creates potential difference that drives charge movement (current).
The higher the voltage, the more energy each charge carries.
Determines how much power a circuit delivers: P = V × I
Voltage is the push (energy per charge).
Current is the flow (charge per second).
A 9V battery with a broken circuit has voltage but zero current.
Voltage drops across components as current flows through them.
The voltage drop tells you how much energy each charge loses (converted to heat, light, motion, etc.).
Voltages in series sum to the battery voltage (KVL).
Once you understand voltage as energy per charge, everything else clicks into place:
All of these rest on the foundation: voltage is the electric field's ability to push charge and deliver energy.