Electromotive force (e.m.f.)
The electromotive force (e.m.f.), ε, of a source is the total electrical energy supplied to each coulomb of charge that passes through it. Like p.d., it is measured in volts (V). The e.m.f. of a cell can be read as the voltmeter reading across its terminals when no current flows (the open-circuit voltage).
Internal resistance
Every real cell has some internal resistance, r, due to the chemicals inside it. When current I flows, some energy is wasted as heat inside the cell, so the useful terminal potential difference, V, is less than the e.m.f. The energy equation is:
Key formula
ε = V + I r and ε = I (R + r)
ε = e.m.f., V = terminal p.d., I = current, r = internal resistance, R = external resistance. The term I r is the 'lost volts'.
As the current drawn increases, the lost volts I r increase, so the terminal p.d. falls. When the circuit is open, I = 0 and V = ε.
Worked example
A cell of e.m.f. 1.5 V and internal resistance 0.5 Ω is connected to an external resistor of 2.5 Ω. Find the current and the terminal p.d.
Current: I = ε / (R + r) = 1.5 / (2.5 + 0.5) = 0.5 A.
Lost volts: I r = 0.5 × 0.5 = 0.25 V.
Terminal p.d.: V = ε − I r = 1.5 − 0.25 = 1.25 V.
Remember
- E.m.f. is measured with no current flowing (open circuit).
- Terminal p.d. is always ≤ e.m.f. once current flows.
- 'Lost volts' = I r, the energy wasted inside the cell.