Electricity — Part 2: Resistance, resistivity and combinations of resistors: visual lesson, CBSE Class 10 Science

Lesson

Resistance and resistors

Part 2 — what decides the resistance of a wire, the idea of resistivity, and how resistors behave when joined in series and in parallel.

In this lesson you will

Relate resistance to length, area of cross-section and material
Use R = ρl/A to calculate resistance and resistivity
Calculate equivalent resistance, current and potential difference in series, parallel and combined circuits
Explain why household appliances are connected in parallel

Diagram

What decides resistance?

For a wire at a given temperature, resistance is proportional to its length $l$ and inversely proportional to its area of cross-section $A$ . It also depends on the material.

Concept

Resistivity: a property of the material

Combining both, $R = \rho\,\dfrac{l}{A}$ . The constant $\rho$ (rho) is the resistivity of the material. Its SI unit is the ohm metre (Ω m). It changes with temperature but not with the length or thickness of the sample.

R = \rho \frac{l}{A}, \qquad \rho = \frac{RA}{l}

Alloys have much higher resistivity than pure metals; insulators are about 10¹⁸ or more times higher still.
Material	Resistivity at 20 °C (Ω m), approximate	Type
Silver	$1.6 \times 10^{-8}$	Metal (best conductor)
Copper	$1.7 \times 10^{-8}$	Metal
Aluminium	$2.7 \times 10^{-8}$	Metal
Tungsten	$5.6 \times 10^{-8}$	Metal
Iron	$1.0 \times 10^{-7}$	Metal
Constantan	$4.9 \times 10^{-7}$	Alloy
Nichrome	$1.1 \times 10^{-6}$	Alloy
Glass	$10^{10}$ to $10^{14}$	Insulator
Rubber	$10^{13}$ to $10^{16}$	Insulator

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