EMF and Potential Difference

In an electric circuit, the battery gives energy to charges, and components like lamps use that energy. EMF tells us how much energy each coulomb of charge receives from the source. Potential difference tells us how much energy each coulomb loses across a component.

Key ideas and definitions

• Potential difference (p.d.): the work done (energy transferred) per unit charge between two points. Measured in volts (V).
• Electromotive force (emf): the energy supplied per unit charge by a source (like a battery) around the whole circuit. Also measured in volts (V).

Equations (W = energy in joules, J; Q = charge in coulombs, C):

$$V = \frac{W}{Q} \quad \text{and} \quad \mathcal{E} = \frac{W}{Q}$$

1 volt means 1 joule of energy for each coulomb of charge: $1\,\text{V} = 1\,\text{J C}^{-1}$.

How voltage behaves in circuits

• Series: the p.d. across components adds up to the source emf (energy given by the battery is shared).
• Parallel: the p.d. across each branch is the same as the source p.d.
• For a conducting component, if the current is constant, increasing resistance increases p.d. (linked by $V = IR$).
• A voltmeter measures p.d. It is connected across (in parallel with) the component.

Energy picture (analogy)

Think of charges like water being lifted by a pump, then flowing down through waterwheels. The pump’s “lift” is the emf. Each waterwheel makes the water lose some height — that loss is like the p.d. across a component. All the “height drops” add up to the total “lift.”

Common misconceptions

• “Voltage is used up.” The energy is used; the charge and total emf are not “used up.”
• “EMF and current are the same.” EMF/p.d. is energy per charge (volts); current is charge flow per second (amperes).