Question

Resistance of a metal wire of length 1 m is 46 Ω at 20°C. If the diameter of the wire is 0.5 mm, what will be the resistivity of the metal at that temperature?

Answer 1

GIVEN:

★Length of the wire is 1m.

★Resistance of the wire is 46ohm

★Diameter of the wire is 0.5mm.

★Temperature is 20°C

TO FIND:

★Resistivity of metal wire at that temperature.

ANSWER :

Length of wire (l) =1m

Resistance (R) = 46ohm

Diameter (d) = 0.5mm. = $0.5×10^{-3}$

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So, cross sectional area =

$\large\green{\boxed{Area_{circle}=πr^{2}}}$

=$\dfrac{22}{7}\times(\dfrac{0.5}{2}×10^{-3})^{2}$

=$0.19625×10^{-6}m^{2}$

=$1.9625×10^{-7}m^{2}$

=$2\times10^{-7}m^{2}$ (approx.)

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Now,

$\large\purple{\boxed{\rho=\dfrac{R×A}{l}}}$

where

$\rho$ is the resistivity.

=>$\rho=\dfrac{R×A}{l}$

=>$\rho=\dfrac{46ohm×2×10^{-7}m^{2}}{1m}$

=>$\rho=92 × 10^{-7}ohm-m$

.°. $\rho=9.2×10^{-6}ohm-m$

Hence the resistivity at 20°C is $9.2×10^{-6}ohm -m$

$\huge\orange{\boxed{\rho=9.2×10^{-6}ohm-m}}$