E.m.f. and internal resistance · Year 13
Real batteries are not perfect: some energy is wasted inside them because of their internal resistance r. The electromotive force (e.m.f.) ε is the total energy given to each coulomb; the terminal p.d. is what is left for the circuit. That is why a battery’s voltage drops when a big current is drawn – like car headlights dimming when the engine starts.
Key facts
- ε = V + Ir, so terminal p.d. V = ε − Ir. The “lost volts” are Ir.
- ε = I(R + r), so I = ε ÷ (R + r).
- With no current flowing, a voltmeter across the terminals reads ε.
- A graph of V against I is a straight line: y-intercept = ε, gradient = −r.
- Cells in series: e.m.f.s add and internal resistances add.
- Maximum power is delivered to the external resistor when R = r.