Question

A wire is stretched to four times it's original length.Calculate it's resistivity.please show the steps

Answer 1

Thanks for requesting.

We have

Resistance= Resistivity x length/area

When the wire is stretched to four times the length , the area of cross section gets reduced to half.

So

New Resistance = Resistivity x 4length/area/4

I.e,

New resistance = (Resistivity x area/length)x16

i.e, New resistance = Resistance x 16

So when the wire is stretched, the resistance multiplies by sixteen times.

Answer 2

Hola mate

Here is your answer -

If you stretch the wire it's resistivity will not change (all because it depends upon nature of wire and temperature only) but also it's volume remains constant so cross section area also changes. As the volume remains constant natural cross section area × natural length = new cross section area × 4× natural length( as the wire is stretched four times) . So new cross section area = natural cross section area / 4

Now assuming that you are aware with the formula for calculating the resistance if length resistivity and cross section area us given which is R = π L/A where π is resistivity , l is length and A is cross section area . Let the natural resistance be R. So

R = πL/A (EQUATION 1)

R (New resistance) = π4L /(A÷4)

= 16πL/A (EQUATION 2)

Divide both the equations and you get will get new resistance equal to 16 times the given resistance.