Current Electricity — Part 2: Cells and combinations of resistors: visual lesson, ICSE Class 10 Physics (Science Paper 1)

Lesson

Inside the cell, and many paths

Part 2 — a cell is not a perfect source: some of its push is used up inside it. And real circuits join resistors one after another or side by side.

In this lesson you will

Distinguish the e.m.f. of a cell from its terminal voltage
Use E = I(R + r) and V = E − Ir
Derive and use the equivalent resistance of resistors in series and in parallel
Find currents and potential differences in a simple series–parallel network

Table of everyday questions and the idea each one uses
Question	Idea used
Why does a torch dim as its cells age?	Internal resistance rises
Why do fairy lights go dark together?	Series connection
Why do room lamps work independently?	Parallel connection
How much current does the battery give?	Equivalent resistance

Concept

E.m.f. and terminal voltage

Electromotive force (e.m.f.), E: the work done by the cell in moving a unit positive charge round the whole circuit, including the cell; it equals the p.d. across the terminals when no current is drawn (open circuit). Terminal voltage, V: the p.d. across the terminals when the cell supplies current. Because the cell has internal resistance r, part of the e.m.f. (the lost volts, Ir) is used inside it, so V < E while current flows.

Table comparing the electromotive force and the terminal voltage of a cell
Feature	E.m.f. (E)	Terminal voltage (V)
When measured	No current drawn	Current being drawn
Value	Fixed for the cell	Less than E; falls as I rises
Depends on	Materials of electrodes and electrolyte	E, the current and r

Diagram

Internal resistance in a circuit

The cell behaves like an ideal e.m.f. E in series with a small internal resistance r. The current is $I = \dfrac{E}{R + r}$ , so $E = I(R + r) = IR + Ir$ , that is e.m.f. = terminal voltage + lost volts, $V = E - Ir$ . Internal resistance increases with the distance between the electrodes and the concentration of the electrolyte, and decreases with a larger area of electrodes in the electrolyte and a higher temperature.

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