Question

a wire having resistance of 3 ohm is stretched to double of its initial lenght calculate the new resistance of the wire
​

Answer 1

Explanation:

ANSWER

Given: a wire of resistance 1Ωis stretched to double its length.

To find the new resistance

Solution:

Here,

R=1Ω,Length=L,Cross sectional area, CSA=A

The formula used is,

R=ρ

A

L

⟹ρ

A

L

=1..........(i)

The new length, L

′

=2L

And new CSA = A

′

So we have,

Volume of the wire= AL

Now after the act of stretching the volume remains constant.

Therefore, AL=A

′

L

′

⟹AL=2LA

′

⟹A

′

=

2

A

Now the new resistance of the wire becomes

R

new

=ρ

A

′

L

′

⟹R

new

=ρ

2

A

2L

⟹R

new

=4ρ

A

L

R

new

=4×1 by using equation (i)

Therefore the new resistance is 4Ω

Answer 2

Explanation:

Resistance,R = pl/A

where,

1) p = resistivity of the wire

2) l = length of wire

3) A= cross section of the wire