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? Hint: Be sure to use the K value found in the reference. (Round the FINAL answer to two decimal places.)

Answer 1

Answer:

Length of the wire = 145.84 m

Step-by-step explanation:

Given : You wish to use #18 tungsten wire at 20°C to make a 10 Ω resistor.

To find : Length of wire will be required for this job.

Solution :

The #18 tungsten has a radius of $r=5.1\times10^{-4}m$.

The resistivity of the tungsten at 20° is $\rho=5.6\times10^{-8}\Omega m$.

The formula that relates resistance and resistivity is

$R=\rho\frac{L}{\pi r^2}$

where L is the length of the wire, R is the resistor, $\pi r^2$ its section and $\rho$ is the resistivity .

Now, we can calculate L :

$L=\frac{R\pi r^2}{\rho}$

$L=\frac{(10)(3.14)(5.1\times10^{-4})^2}{5.6\times10^{-8}}$

$L=\frac{816.714\times10^{-8}}{5.6\times10^{-8}}$

$L=\frac{816.714}{5.6}$

$L=145.84 m$

Therefore, Length of the wire = 145.84 m