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Question

(a) What do you understand by the " resistivity" of a substance
(b) A wire is 1.0 m long, 0.2 mm in diameter and has a resistance of 10 Ω Calculate the resistivity of its material?

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Solution

(a)
Resistivity or specific resistance of a body is a characteristic by which one can judge the electrical property of a substance. As the name suggests, resistivity is associated with the resistance to electrical flow of electrons. Resistivity quantifies how strongly a material opposes the flow of electrons through it.

If a material has low resistivity, it means it offers less resistance to the electric current. This implies that a material with low resistivity has highly conductive​. For example, Silver!

In terms of definition, resistivity is defined as the resistance of a of a material of unit cross section and unit length.

We know that resistance can be written as:

R = ρ L/A

Where ρ is a the resistivity of the substance.

This clearly means that.. resistivity of a substance is moreover same for any length or cross section area, whereas the resistance can vary!


(b)
H e r e space comma space i t space i s space G i v e n space t h a t colon l equals 1 m space comma d equals 0.2 m m rightwards double arrow r equals 0.1 m m space a n d space R equals 10 space o h m b y space u sin g space F o r m u l a e R space equals space rho space L over A R space equals space rho fraction numerator 1 over denominator straight pi cross times open parentheses 0.1 cross times 10 to the power of negative 3 end exponent close parentheses squared end fraction rho space equals space R space cross times straight pi cross times open parentheses 0.1 cross times 10 to the power of negative 3 end exponent close parentheses squared rho space equals space 3.14 space cross times 10 to the power of negative 7 end exponent space capital omega to the power of negative 1 end exponent m to the power of negative 1 end exponent


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