Question

A wire of length 4m and radius 0.25mm has a resustance of 24ohm. Find the resistivity of the wire .​

Answer 1

Explanation:

Resistivity = (R x A)/length

Radius = 0.25mm = 0.00025 m

length = 75m

Resistance = 10 ohms

Area of cross section = πr^2

= 22/7 x 0.00025 x 0.00025

Resistivity =

(10 x 22/7 x 0.00025 x 0.00025 ) ÷ 75

= (220/7 x 0.00025 x 0.00025)/75

= 2.63 x 10 to the power (-8) ohmmeter

Answer 2

A wire of length 4m and radius 0.25mm has a resistance of 24ohm, the resistivity of the wire is 0.0011.

Given:

length(L) = 4m

radius = 0.25mm

resistance(R) = 24Ω

To find:

Resistivity = ?

Solution:

Resistivity:

• This is the measure of power of opposition of flow of current through any particular material or conductor with uniform cross-section.
• Resistivity is generally the reciprocal quantity which measures how easily particular material allows the electric flow. It is denoted by 'ρ'.

Formula to be used:

ρ = $\frac{RA}{L}$

Here, ρ = resistivity of wire, R = resistance, A = area of cross-section and L = length of wire

Area = $\pi r^{2} = \pi (0.25)^{2} = 0.196mm^{2}$

ρ = $\frac{(24)(0.196)}{4000} = 0.0011$

Therefore, a wire of length 4m and radius 0.25mm has a resistance of 24ohm, the resistivity of the wire is 0.0011.