Voltage: energy per charge

Voltage is energy per unit charge

This is the single most useful idea in this whole topic, so it's worth sitting with: voltage isn't a "thing" flowing through the wire — current is the thing that flows. Voltage is a measure of how much energy every coulomb of that charge is carrying, or how much energy it gives up, at a particular point.

V = W / Q

Where V is voltage in volts (V), W is energy transferred in joules (J), and Q is charge in coulombs (C). One volt means one joule of energy is transferred for every coulomb of charge: 1 V = 1 J/C.

EMF vs. p.d. — same formula, two different jobs

You'll meet two names for voltage, and they describe opposite ends of the same journey:

• EMF (electromotive force) is the energy the battery gives to each coulomb of charge — it's the "push". Symbol is still volts.
• p.d. (potential difference) is the energy a component takes away from each coulomb as charge passes through it — spent on light, heat, or whatever that component does.

In the circuit below, there's only one resistor for the charge to pass through. Every joule the battery gave out has to be spent somewhere before the charge gets home — and there's only one place to spend it. So the p.d. across that resistor always equals the battery's EMF, no matter what you set the resistance to.

Measuring voltage: the voltmeter

A voltmeter measures p.d. and connects in parallel — across a component, tapping both its ends, not sitting in the charge's path at all. A good voltmeter has an extremely high resistance, so almost no current takes the detour through it. That's why the ammeter and voltmeter are drawn so differently above: one interrupts the wire, the other sits beside it.

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