Question

A resistance wire of length I and resistance R is stretched such that its radius has reduced to one third of original value. what is the new resistance?​

Answer 1

As we know,

R=

A

ρL

..........(i)

If you stretch the wire till it's radius is halved the previous value, then it's length will increase 4 times to keep the volume constant.

So, new values are,

L

2

=4L

A

2

=

4

A

where, L and A are the values of original length and area

Resistivity remains the same as it depends upon the material of the wire.

So, the new resistance will be,

R

1

=

A

ρL

R

1

=

A/2

ρ4L

R

1

=

A

16ρL

R

1

=16R