Electromotive Force and Potential Difference

Definition

Electromotive force (e.m.f.) is the work done per unit charge by a source in driving charges around a complete circuit.

In symbols, $$E = \dfrac{W}{Q}$$ and it is measured in volts (V), with \(1\,\mathrm{V} = 1\,\mathrm{J\,C^{-1}}\).

When several sources are connected in series and oriented in the same direction, the total e.m.f. is the sum of their individual e.m.f.s: \(E_{\text{total}} = E_1 + E_2 + \cdots\). For example, three identical cells of \(1.5\,\mathrm{V}\) in series provide \(E_{\text{total}} = 1.5 + 1.5 + 1.5 = 4.5\,\mathrm{V}\). If one source is reversed, it opposes the others and its e.m.f. subtracts; for instance, \(1.5 + 1.5 - 1.5 = 1.5\,\mathrm{V}\).

Definition

📖 Potential difference (p.d.) across a component is the work done per unit charge in driving charges through that component.

In symbols, $$V = \dfrac{W}{Q}$$ and it is measured in volts (V), indicating energy transferred per coulomb across the component.

In analysis and problem solving, the source e.m.f. sets the energy provided per coulomb to the circuit, while the p.d. across components accounts for the energy used or transferred in those parts of the circuit. In a simple series circuit, the sum of the p.d.s across the components equals the e.m.f. of the source, reflecting energy conservation.

Quick Quiz: E.M.F & P.D.

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