Question

You wish to use #18 tungsten wire at 20°c to make a 10 ω resistor. what length of wire will be required for this job? (round the final answer to two decimal places.)

Answer 1

The #18 tungsten has a radius of
`r=5.1\cdot 10^(-4)m`. The resistivity of the tungsten at
`20^(\circ)` is
`\rho=5.6\cdot 10^(-8) \Omega m`. The formula that relates resistance and resistivity is

`R=\rho (L)/(\pi r^2)`
where L is the length of the wire and
`\pi r^2` its section. Therefore, we can calculate L:

`L= (R \pi r^2)/(\rho)= (10\Omega \cdot \pi (5.1\cdot 10^(-4)m)^2)/(5.6\cdot 10^(-8) ) =145.8 m`