First slide

Resistivity and conductivity

Question

An aluminium (resistivity $ρ = 2.2 \times 10^{- 8} Ω - m$ ) wire of a diameter $1.4 m m$ is used to make a $4 Ω$ resistor. The length of the wire is

Easy

A

$220 m$
B

$100 m$
C

$280 m$
D

$1 m$

Solution

Resistivity $ρ = 2.2 \times 10^{- 8} Ω - m$
Diameter $D = 1.4 \times 10^{- 3} m$

Radius $r = 0.7 \times 10^{- 3} m$

Resistance $R = 4 Ω$

Length $l = ?$

Length of the wire is

$l = \frac{R A}{ρ}$

$= \frac{4 \times π \times {(0.7 \times 10^{- 3})}^{2}}{2.2 \times 10^{- 8}}$

$∴ l = 280 m$ .

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