Question

Hen a thin copper wire that is 178 m long is connected between a 1.2-v potential difference, a current of 2.0 amps flows through the wire. what is the diameter of this wire? the resistivity of copper is 1.72 × 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)` .

From the above 2 equations,

`image`

The resistance of the wire is given by

`image`

Thus, the diameter of the wire is

`image`

The diameter of the wire is
`2.55 \;mm`