A level Physics · Edexcel 9PH0 · Topic 3E

EMF and internal resistance

Key points

E.m.f. ( $\varepsilon$ ) is the energy transferred into electrical energy per unit charge by a source, measured in volts.
Real sources have internal resistance $r$ , so some energy is wasted inside: $\varepsilon = I(R + r)$ or $\varepsilon = V + Ir$ .
The terminal p.d. $V$ is less than the e.m.f. when current flows; the difference $Ir$ is called the lost volts.
Core practical: vary the external resistance and plot terminal p.d. $V$ against current $I$ . The graph $V = -rI + \varepsilon$ is a straight line with gradient $-r$ and $y$ -intercept $\varepsilon$ .
A low internal resistance lets a battery deliver large currents (e.g. car batteries); a high internal resistance limits current, which is safer for EHT supplies.
Open circuit ( $I = 0$ ): terminal p.d. equals the e.m.f.
Maximum power is delivered to the external load when $R = r$ .

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Real cells and power supplies are not perfect: some energy is transferred inside them, so the p.d. they deliver falls as the current rises. These notes cover e.m.f., internal resistance and core practical 3.

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