Question

What must be the diameter of a cylindrical 120-m long metal wire if its resistance is to be ? The resistivity of this metal is 1.68 × 10-8 Ω • m.

Answer 1

The diameter is
`d = 6.5 *10^(-4) \ m`

Step-by-step explanation:

From the question we are told that

The length of the cylinder is
`l = 120 \ m`

The resistance is
`\ 6.0\ \Omega`

The resistivity of the metal is
`\rho = 1.68 *10^(-8) \ \Omega \cdot m`

Generally the resistance of the cylindrical wire is mathematically represented as

`R = \rho (l)/(A )`

The cross-sectional area of the cylindrical wire is

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

Where d is the diameter, so

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

=>
`d = \sqrt{ \rho* (4 * l )/(\pi * R ) }`

`d = \sqrt{ 1.68 *10 ^(-8)* (4 * 120 )/(3.142 * 6 ) }`

`d = 6.5 *10^(-4) \ m`