Question

A gold wire has a cross-sectional area of 1.0 cm^2 and a resistivity of 2.8 × 10^-8 Ω ∙ m at 20°C. How long would it have to be to have a resistance of 0.001 Ω?

Answer 1

Length, l = 3.57 meters

Step-by-step explanation:

It is given that,

Area of cross-section of gold wire,
`A=1\ cm^2=0.0001\ m^2`

Resistivity of gold wire,
`\rho=2.8* 10^(-8)\ \Omega-m`

Resistance, R = 0.001 ohms

Resistance in terms of length and area is given by :

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

`l=(RA)/(\rho)`

`l=(0.001* 0.0001)/(2.8* 10^(-8))`

l = 3.57 meters

So, the length of the wire is 3.57 meters. Hence, this is the required solution.