Why is the resistance of a wire vary with its area of cross - section?

1.	Why is the resistance of a wire vary with its area of cross - section?
Answer» Resistance: Resistance of a wire is directly proportional to the length of the conductor and inversely proportional to the area of the cross-section. That is, \(R\propto\frac{L}{A}\) Introducing a constant of proportionality, \(R=\frac{\rho L}{A}\)(where \(\rho\) is the resistivity of the material.) 1. From the formula, we can observe that the resistance is inversely proportional to the cross-section area. 2. Hence, the resistance increases as the cross-section area decreases and vice-versa.

Answer»

Resistance: Resistance of a wire is directly proportional to the length of the conductor and inversely proportional to the area of the cross-section.

That is, \(R\propto\frac{L}{A}\)

Introducing a constant of proportionality,

\(R=\frac{\rho L}{A}\)(where \(\rho\) is the resistivity of the material.)

1. From the formula, we can observe that the resistance is inversely proportional to the cross-section area.
2. Hence, the resistance increases as the cross-section area decreases and vice-versa.

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