Change of Resistance in Wires by Stretching

Last Updated on October 25, 2023 by Electricalvolt

We shall understand with an example how the resistance of a wire changes with stretching its length.

Example-1 –Change of Electrical Resistance with wire stretching

The resistance of L length wire is R. If half of its length stretch such as the total length becomes 2L what will be the final resistance?

resistance after stretching of wire

 

The resistance of L length wire is R.


The resistance of L/2 length wire is R/2

Now the other L/2 length of the wire is stretched to length X to have full length of conductor 2L

L/2 +X = 2L

X= 3/2 L

The length of the stretched conductor is 1.5 L.

Length of conductor L/2  is stretched up to 1.5 L, the length of the stretch conductor is now 3 times of the original length hence the diameter of the conductor is d/3. The resistance of the stretched conductor.

R1=  x L/A 

 x L/πd2 

= 3 /(1/9)

R1= 27 times of the original resistance of the half length wire

R1= 27 x R/2 =13.5 R

The resistance of conductor after stretching is

= R/2 + 13.5 R= 

= 14 R

The new resistance of the wire after stretching its half length is 14 times of the original resistance of conductor.

Example-2 

What is the  new resistance of a wire if it is stretched to twice its original length. Original resistance is 10 ohm. 

After stretching of wire

Length of wire L1 = 2 L
New Area A1 = A/2

In above conditions,the volume of the wire remain the same.

New Resistance R1 = ρ L1 /A1

                                 = ρ x 2L /A/2

                                  = ρ x 4L /A

                             R1 = 4 ρ L /A

                                  = 4 R = 4 x 10

                            R1 = 40Ω

New resistance will be 4 times of the original resistance

Example-3 

A wire has a resistance of 30 ohms. We stretch the wire by  10% of its original length, what will be the new resistance?

Let the  original length and area of a wire is L and A respectively.

The resistance of wire R = ρ L /A

After 10 % stretching  the length and area of wire is L1 and A1

L1 = 1.1 L
 The volume must remain the same after stretching

A1 = (1/1.1 )A = 0.909 A

The new resistance of wire

R1 = ρ L1/A1

     = ρ (1.1L)/ (0.909 A)

    R1  = 1.21 ρ L /A = 1.21R

         = 1.21 x 30
    R1 = 36.3 Ω

The above illustrative examples shows how the resistance of a wire changes with stretching its length.

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