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
$R=\rho \frac{L}{\pi r^2}$
where L is the length of the wire and $\pi r^2$ its section. Therefore, we can calculate L:
$L= \frac{R \pi r^2}{\rho}= \frac{10\Omega \cdot \pi (5.1\cdot 10^{-4}m)^2}{5.6\cdot 10^{-8} } =145.8 m$