CBSE Class 10 Science 2019 · Paper 31/3/1 · Question 20(b)

Electricity 5 marks Medium

(a)Write the relation between resistance and electrical resistivity of the material of a conductor in the shape of a cylinder of length ‘ $l$ ’ and area of cross-section ‘A’. Hence derive the S.I. unit of electrical resistivity.
(b)Resistance of a metal wire of length $5$ m is $100 Ω$ . If the area of cross-section of the wire is $3 \times 1 0^{- 7} m^{2}$ , calculate the resistivity of the metal.

Answer

$R = ρ \frac{l}{A}$ , so the SI unit of $ρ$ is ohm metre; for the wire $ρ = 6 \times 1 0^{- 6} Ω m$ .

(a) The resistance of a cylindrical conductor is directly proportional to its length and inversely proportional to its area of cross-section,

R \propto \frac{l}{A}

, so

R = ρ \frac{l}{A}

, where

ρ

is the electrical resistivity of its material. Hence

ρ = \frac{R A}{l}

, and its SI unit is

\frac{Ω \times m ^{2}}{m} = Ω m

(ohm metre). (b)

ρ = \frac{R A}{l} = \frac{100 Ω \times 3 \times 1 0 ^{- 7} m ^{2}}{5 m} = 60 \times 1 0^{- 7} Ω m = 6 \times 1 0^{- 6} Ω m

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