What happens to the total resistance in a wire if its cross-sectional area is increased by four times?

In electrical circuits, resistance is influenced by the cross-sectional area of a conductor. According to the formula for resistance ( R ), which is given by:

[

R = \frac{\rho L}{A}

]

where ( R ) represents resistance, ( \rho ) is the resistivity of the material, ( L ) is the length of the conductor, and ( A ) is the cross-sectional area.

When the cross-sectional area ( A ) is increased by four times, the new resistance can be calculated. Since resistance is inversely proportional to the cross-sectional area, increasing the area by a factor of four will decrease the resistance by the same factor.

Thus, if the original resistance is ( R ), the new resistance after increasing the area becomes:

[

R' = \frac{\rho L}{4A} = \frac{R}{4}

]

This indicates that the total resistance becomes one-fourth of the original resistance. Hence, when the cross-sectional area is increased by four times, the total resistance in the wire is one-fourth of what it was originally.