Answer to Question #169684 in Electric Circuits for Anton

Question

Assume you need a 5.0 ohms resistor and you have available #22 guage wire with a diameter of 6.38 ×10^-4 m.compute the length of wire needed for the resistor.

Answer 1

The resistance is:

$R=\rho\frac{l}{A}=\rho\frac{4l}{\pi d^2},$

where $\rho$ - the resistivity of a material (for copper $\rho=1.724\cdot10^{-8}\space Ohm\cdot m$ );

l - the length of wire;

A - the cross-sectional area of wire;

d - the diameter of wire;

$l=\frac{\pi d^2R}{4\rho}=\frac{3.14\cdot (6.38\cdot 10^{-4})^2\cdot5}{4\cdot1.724\cdot 10^{-8}}=92.7\space m.$

Answer: 92.7 m.