What e.m.f. and internal resistance mean

The electromotive force, or e.m.f., of a cell is the energy it supplies to each coulomb of charge driven around the circuit. It is the full voltage of the cell when no current flows.

But a real cell is not perfect. Its chemicals and materials resist the current too, and this is called internal resistance. When current flows, some energy is spent pushing charge through the cell itself, warming it slightly. The voltage left for the outside circuit, the terminal voltage, is therefore a little less than the e.m.f., and it drops further as more current is drawn.

This is why a torch dims when its battery is old, and why a car's headlights dim briefly when the starter motor draws a huge current: the large current causes a big loss across the internal resistance.

In SPM you should distinguish e.m.f. from terminal voltage and explain the drop using internal resistance.

Electricity

The physics behind it

The electromotive force (e.m.f.), symbol ε, of a cell is the energy it supplies to each coulomb of charge driven round the whole circuit, measured in volts (V). A real cell also has internal resistance, r, in ohms (Ω), because its own materials oppose the current.

When a current I flows, the cell drives charge through both the external resistance R and its own r, so the e.m.f. splits into two parts: ε = IR + Ir = I(R + r).

The terminal voltage, V = IR, is what the outside circuit actually receives, and it is always a little less than ε once current flows, because Ir is lost inside the cell. For a cell of ε = 1.5 V and r = 0.5 Ω connected to R = 2.5 Ω, the current is I = ε/(R + r) = 1.5 V / (2.5 Ω + 0.5 Ω) = 0.5 A, and the terminal voltage is V = IR = 0.5 A × 2.5 Ω = 1.25 V, below the 1.5 V e.m.f.

The larger the current, the bigger the internal loss Ir.

See it in daily life

An old torch that grows dim shows internal resistance at work. As a dry cell ages, its internal resistance rises, so more of the e.m.f. is lost inside the cell and less terminal voltage reaches the bulb, which fades.

A striking case is starting a car: the moment you turn the key, the starter motor draws a very large current, and that big current across the battery's small internal resistance causes a noticeable Ir drop, so the headlights or dashboard lights dim for a second before recovering.

You also feel it when several cells grow warm after heavy use: the energy lost as Ir inside them turns into heat. This is why a battery labelled 1.5 V rarely delivers a full 1.5 V to a working circuit; the terminal voltage you measure while current flows is always a little lower than the e.m.f. printed on the cell.

The heavier the load, the larger the current, and the bigger the gap between e.m.f. and terminal voltage becomes.

How this comes up in SPM

This topic sits in the Form 5 Electricity chapter, extending potential difference and Ohm's law. Paper 2 asks you to Define e.m.f. as the energy per unit charge supplied by the source, and to Distinguish it from terminal voltage.

You are often asked to Explain why the terminal voltage falls when current increases, naming the internal resistance and the Ir loss.

Calculation questions require you to use ε = I(R + r) to Determine the current, the internal resistance, or the terminal voltage, so units on every line are expected. A common practical asks you to Plot terminal voltage V against current I, then Determine the e.m.f. from the intercept and the internal resistance from the gradient.

Neighbouring standards include potential difference, resistance, and series and parallel circuits. Command words such as Define, Distinguish, Explain, Determine and Plot recur.

Writing that the terminal voltage equals the e.m.f. while current flows is a common error, so always account for the internal resistance.

Source: DSKP KSSM Physics Form 4 and 5 (Versi English) (Bahagian Pembangunan Kurikulum (BPK), KPM)