Question

The resistivity of copper is 1.7 X 1O^-8 ohm m. What length of copper wire of diameter 0.1 mm will have a resistance of 34 ohm?

Answer 1

Resistance `R` of a conducting wire of length `l` and of area of cross section `A` is given by the expression

`R=rhol/A`
where `rho` is resistivity or specific resistance of the material of the conductor.

Inserting given values in the expression in SI units we get

`34=(1.7 xx 10^-8)l/(pi(0.1/(1000))^2/4)`
`=>l=34/(1.7 xx cancel(10^-8))xxpi/4cancel((0.1/(1000))^2)`
`=>l=15.71\ m`, rounded to two decimal places.