Cells, Kirchhoff’s Laws, Bridges and Potentiometer

Lesson

Part 1 — what a cell really supplies, how cells are best grouped, and two laws that solve any network.

In this lesson you will

Distinguish the emf of a cell from its terminal potential difference and derive E = I(R + r)
Find the current from series, parallel and mixed groupings of cells, and from two unequal cells in parallel
Apply Kirchhoff’s junction and loop laws to circuits with more than one loop

Concept

Electromotive force (emf)

A cell uses chemical energy to move charge from its negative to its positive terminal, against the electric field inside it. The emf E is the work done by the cell per unit charge taken once round the complete circuit: $E = \dfrac{W}{q}\qquad(\text{unit: J C}^{-1} = \text{V})$

Emf is not a force: it is energy supplied per coulomb.
On open circuit (no current) the terminal p.d. equals E.

Diagram

Internal resistance and terminal potential difference

The electrolyte and electrodes have an internal resistance r. With an external resistor R, energy conservation per coulomb gives $E = IR + Ir = I(R + r),\qquad V = IR = E - Ir$

Ir is the “lost volts”: energy per coulomb turned to heat inside the cell.
While the cell is being charged (current forced in at the + terminal): $V = E + Ir$ .

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