A wire is stretched to double its length .what will be its new Resistance?

 Resistance is opposition offered by material to the flow of charges. In this article we will discuss if a wire is stretched to double its length then what will be its new Resistance?

so to understand this take an example we have a wire of resistance of value Rohm and length L and area A.

Now as per above question if length of wire is double then what will the new resistance?

So to understand this we need to understand below concept. As we know the volume is given by Area*Length so please refer below mathematical expression.

         V=A*L  here V is volume of wire,A is area and L is length of wire.

        L=V/A  from above equation.    ..........1

also A=V/L.................2

now if length of wire is double then we have equation 

2L=V/A now from here we will calculate the area.

A=V/2L .........equation no.3

from equation number 3 we understand that if length is double the area of wire is half so to understand the effect of resistance please follow below equations.

We know that we can write resistance as 

R=ρ L/A

so put value of A from equation number 2

R=ρ L/V/L

R=ρ L*L/V............4

so from equation number 4 we get the resistance value in initial condition now take second case if length is double.

Let us consider the new resistance is R1 then

R1=ρ  2L*2L/V

R1=ρ 4L*L/V

R1= 4ρ L*L/V..........5

now if you see equation 4 R=ρ L*L/V so know from here put this value in equation number 5 we get


so the new resistance will be 4time of initial resistance.

A wire is stretched to double its length then the new resistance will be 4time of initial resistance.

Both the parameters length,area depends up on each other if we stretch the length of wire area of wire will decrease.

so we hope friends you will understand above topic if you have any query please comment below.

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