#### Question

If the length of a wire is doubled by taking more of wire, what happens to its resistance?

#### Solution

We know that the resistance of the wire,

*R*= ρ*l**/**A*where the resistivity of the wire is ρ.The length of the wire =

The area of cross-section of the wire,

*l*The area of cross-section of the wire,

*A*= π*r*^{2}So when the length of the wire is doubled (

*l' = 2l*) by taking more of the same wire, (it will keep the resistivity and the area of cross-section the same), the length is doubled.New resistance =

*R'**R'*= ρ

*l*

*'*/

*A*

*R'*= 2ρ

*l*

*/*

*A*

*R'*= 2

*R*

Is there an error in this question or solution?

Solution If the Length of a Wire is Doubled by Taking More of Wire, What Happens to Its Resistance? Concept: Resistance of a System of Resistors - Resistors in Series.