Question

The length of a metal wire is drawn and doubled. How many times will the new resistance of the wire become?

Answer 1

We know that resistance of wire depend on its length and cross sectional area.Mathematically

$$R=\rho\frac{l}{A}$$

Where R is resistance of wire, l is length of wire ,A is cross sectional area and $\rho$ is resistivity of metal.

Note that after stretching wire its cross sectional area and length varies but Its volume$(Al=constant)$remain constant.It means that If length is doubled , automatically its cross sectional area is halved. Thus New resistance of wire

$$R_{new}=\rho\frac{{2l}}{\frac{A}{2}}$$

$$R_{new}=4\rho\frac{l}{A}=4R$$

Thus New resistance of wire is 4 times of the initial value.