Question

The resistance of the wire when the length of the wire increases four times without changes its volume is​

Answer 1

Answer:

Resistance of the wire when the length of the wirw increase four times without changes its volume is 16R

Explanation:

Let the Resistance of the wire is R

Length of wire is L

Area of wire is A

As we know that , R = ρL/A ________(1)

When length of the wire increases 4times .

Then , length of new wire L' = 4L

Area of wire A , when length increases 4times

Area A' , ∴ A' L' = A L

A' 4 L = AL

A' = A/4

Since, new resistance R' = ρ 4L/A/4

R' = ρ16L/A __________(2)

• from (1) and (2)

• R/R' = 1/16

• R' = 16R

Answer 2

Answer:

The resistivity of the wire is do not depends on the length of the wire.

• The Resistivity is equals to the length per unit area of the wire through which the current is passes.

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

Where, R= resistivity of the wire

l= length of the wire

A= area of cross section of wire.

Explanation:

If  the length of the wire increases four times without changes its volume then,

$2\pi r1^{2}\times l =2\pi r2^{2}\times 4l$

so, $R=\frac{l}{4l}$

so the resistance becomes 1/4 the initial resistance.