KCET 2025 Physics Paper

To understand how the resistance of a metal wire varies with its diameter, while keeping other factors like length and temperature constant, we use the formula for resistance:
R=‌

ρℓ

A

=‌

ρℓ

πr2

Where:
R is the resistance.
ρ is the resistivity of the material.
ℓ is the length of the wire.
A is the cross-sectional area of the wire.
r is the radius of the wire.
Since A=πr2, the resistance R is inversely proportional to the square of the radius:
R∝‌

1

r2

When considering the diameter d of the wire, which is twice the radius ( d=2r ), the relation can be rewritten in terms of the diameter:
R∝‌

1

(d∕2)2

=‌

4

d2

This indicates that as the diameter of the wire increases, the resistance decreases quadratically. The relationship between resistance R and diameter d is a hyperbolic function, as resistance is inversely proportional to the square of the diameter.