Question

How does the resistance $\left(R\right)$ of a wire depend on its radius r ?

• A. $R\propto \frac{1}{r}$
• B. $R\propto \frac{1}{r^2}$
• C. $R\propto r^2$
• D. $R\propto r$

Answer 1

The correct option is B $R\propto \frac{1}{r^2}$

The electrical resistance of an electrical conductor is the opposition to the passage of an electric current through that conductor.
The resistance of a wire is inversely proportional to the area of cross section of the wire. Since the area of the cross section of wire is proportional to the square of radius, the resistance of the wire is inversely proportional to square of the radius of the wire.
Hence, the resistance of wire decreases as the diameter of the wire increases and the resistance of the wire increases as the diameter of the wire decreases.