Electromotive Force (EMF)

Electromotive force (EMF) is the energy a source (like a battery or generator) gives to each coulomb of charge to move it around a complete circuit. It tells us how much “electric push” the source provides. EMF is measured in volts (V).

What is EMF?

Definition: The EMF of a source is the work done (energy transferred) per unit charge as the charge goes once around the whole circuit. Think of a water pump lifting water to a higher level so it can flow. The battery is the pump for charges: it raises their energy.

Important: Despite the name, EMF is not a force. It is energy per charge. The name is historical.

Equation and Units

The equation for EMF is:

$$\varepsilon = \frac{W}{Q}$$

Where $\varepsilon$ is EMF in volts (V), $W$ is energy (work done) in joules (J), and $Q$ is charge in coulombs (C). One volt means one joule of energy for each coulomb of charge: $1\,\text{V} = 1\,\text{J C}^{-1}$.

EMF vs Potential Difference (p.d.)

• EMF: across the source (battery/generator). It is the energy supplied per coulomb to the circuit.
• p.d.: across a component (lamp, resistor). It is the energy used per coulomb in that component.
• Both are measured in volts and both use $V = W/Q$. EMF is like the “give”; p.d. is the “take”.
• In real batteries, when current flows, the terminal p.d. can be slightly less than the EMF due to internal resistance. When no current flows, terminal p.d. ≈ EMF.

Real-world connections

• A 1.5 V cell gives 1.5 J to each coulomb of charge. A 9 V battery gives 9 J per coulomb.
• Phone chargers are about 5 V; mains electricity is about 230 V (the generator provides this EMF).
• EMF can also be induced by moving a conductor in a magnetic field (generator principle).