Current Resistance And Electricity

The resistance of a wire is given by the formula: where is the resistivity, is the length, and is the cross-sectional area of the wire. The area of the cross-section of the wire is: When the wire is stretched, the length increases, and the radius is halved. Let the new length be and the new radius be . Since the volume of the wire remains constant (because the wire is just stretched, not material added or removed), the volume before and after stretching is the same: Simplifying: So, the new resistance is: