Question

How does the resistance of a wire vary with its cross-section area?

Answer 1

Resistance is the constraint of the current flow in an electrical circuit. It is measured in Ohms. The formula of the resistance is gained from Ohm’s Law. The resistance can be written in the form of resistivity. From this formula, it is shown that the electrical resistance of a wire depends upon the length, cross-section, and resistivity of the wire.

Complete answer:
Resistance controls the current flow in a circuit. its unit is ohms, symbolized by the Greek letter omega $\left( \Omega \right)$
The formula of resistance in terms of resistivity of a wire is given by,
$R = \dfrac{{\rho l}}{A}$
Where,
$l$is the length of the wire, $A$is the Cross-sectional area of the wire, and $\rho$ is the resistivity.
a) Length:
From the formula, it is seen that the Resistance is directly proportional to the length of the conductor. $R \propto l$ . with the increase of length the amount of resistance increases.
b) Cross-sectional area:
From the formula, it is seen that the Resistance is inversely proportional to the cross-sectional area of the conductor. Thus, the resistance of the conductor decreased with a decrease in cross-sectional area. $R \propto \dfrac{1}{A}$
The resistance is inversely varied with the cross-sectional area of a wire.

Note: It is vital to notice that electrical conductivity and resistivity are inversely proportional, meaning that the more conductive something is that the less resistive it will be.
Resistance is directly proportional to the temperature of the conductor. If the temperature is increased, the resistance is additionally increased.
By utilizing the resistance of a conductor, light is often created in an incandescent light bulb. In an incandescent light bulb, there's a wire filament that's a particular length and width, thus providing a particular resistance.