Define electromotive force (e.m.f.) as the electrical work done by a source in moving a unit charge around a complete circuit

What is Electromotive Force (e.m.f.)?

⚡️ The e.m.f. is the electrical work done by a source (like a battery or generator) in moving a unit charge around a complete circuit.

In mathematical terms: \$\mathcal{E} = \frac{W}{q}\$

where W is the work (in joules) and q is the charge (in coulombs).

The unit of e.m.f. is the volt (V). 1 V = 1 J / C.

Analogy: The Battery as a Water Pump

Imagine a water pump pushing water through a pipe. The pump does work to move the water, giving it a pressure difference. Similarly, a battery does electrical work to push electrons, creating a potential difference (voltage) across its terminals.

🔋 A 1.5 V battery pushes 1 C of charge, doing 1.5 J of work: \$\mathcal{E} = \frac{1.5\,\text{J}}{1\,\text{C}} = 1.5\,\text{V}\$

📚 Tip: If you’re given the work done by a source and the charge moved, simply divide the work by the charge to find the e.m.f. (ℰ). Remember the units: joules divided by coulombs gives volts.

📝 Tip: In questions about a battery, the e.m.f. is often the same as the voltage you read across its terminals when no current is flowing.