Question

What length of a certain metal wire of diameter 0.15 mm is needed for the wire to have a resistance of 15 ω? the resistivity of this metal is 1.68 × 10-8 ω ∙ m?

Answer 1

The resistance of the cylindrical wire is
`R=(\rho l)/(A)`.

Here
`R` is the resistance,
`l` is the length of the wire and
`A` is the area of cross section. Since the wire is cylindrical
`A=(\pi d^2)/(4)` . Rearranging the above equation,

`A=(\rho l)/(R)\\ (\pi d^2)/(4)=(\rho l)/(R)\\ l=(\pi d^2 R)/(4 \rho)`

Here
`d=0.15, R=15, \rho=1.68(10^(-8))`.

Substituting numerical values,

`image`

The length of the wire is
`15.78 \;\;m`