Question

An iron wire has length 8.0m and a diameter 0.50mm. The sir has a resistance R.

A second iron wire has length 2.0m and diameter 1.0mm

What is the resistance of the second wire?

Answer 1

The resistance of the second wire is 16 R.
where R is the resistance of the first wire.

R = ρ
`(l)/(A)`
where l = length of the wire
A = area of the wire
A =
`\pi r^(2)` where, r =
`(diameter of wire)/(2)`

Thus, on finding the ratio of resistance of the two wires, we get,


`(R1)/(R2) = (l1A2)/(l2A1)`

here, R1 = R
l1 = 8m
l2 = 2m
A1=π
`0.25^(2)`
A1=π
`0.50^(2)`

we get. R2 = 16R