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Question

Suppose the resistance of a wire varies inversely as the area of its cross-section. Write a relation between resistance and area of cross-section.


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Solution

Resistance: The opposition that a substance provides to the flow of electric current is referred to as resistance.

Second law of resistance: The resistance of the conductor is inversely proportional to the cross-section area of the conductor.

Step 1: Assumptions:

Let r be the radius of the wire.

Then the cross-section area of the wire is =πr2

Let Ris the resistance of the conductor

Step 2: Find the relation:

R1πr2(From 2nd law of resistance )

R=ρπr2 [ where ρ is some arbitrary constant]

Hence, the relation is R=ρπr2.


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