E.m.f. & Internal Resistance

• The label on a battery is its e.m.f. E: the energy transferred per unit charge in driving charge around a complete circuit.
• That sentence is the definition the mark scheme wants. Learn it exactly as it is written.

• From the Electricity chapter: e.m.f. is energy put in per coulomb, and p.d. is energy taken out per coulomb. The unit is the same; the meaning is opposite. If that feels new, reread the p.d. and e.m.f. page before going on.

• The charge has to push through the inside of the battery: chemicals, plates, connections. They resist. That is the battery's internal resistance r.
• So we model a real battery as a perfect cell E in series with a hidden resistor r, sealed in one box. You can only ever touch the two terminals of the box.

• The voltage you can actually measure, across the terminals, is the terminal p.d. V. It is what the outside circuit receives.
• The volts that disappear inside, across r, are called the lost volts. They heat the battery instead of the circuit. That is why a battery giving a large current feels warm.

E is the energy per coulomb put in by the chemical reactions. V is what is left for the outside circuit. The difference, Ir, is lost inside the battery.

• No new physics here: R and r are simply in series, so the whole loop obeys $I = E/(R+r)$.
• Rearranged: $V = E - Ir$, where $V = IR$ is the terminal p.d. The more current you draw, the more volts are lost inside.

• Both examples used the same method: write $E = IR + Ir$, put in what you know, and solve for the one value you do not know.