Question

If a copper wire with a 0.300 mm diameter is to have a resistance of 0.500 Ω at 20.0ºC, how long should it be? The resistivity of copper is 1.68 * 10^-8 Ω*m

Answer 1

Given:

• Diameter = 0.300 mm

,

• Resistance = 0.500 Ω

,

• Temperature = 20.0ºC

,

• Resistivity = 1.68 * 10⁻⁸ Ω*m

Let's find the length of the copper wire.

To find the length of the wire, apply the formula:

`\begin{gathered} R=(\rho L)/(A) \\ \\ R=(\rho L)/(\pi r^2) \end{gathered}`

Where:

R is the resistance = 0.500 Ω

p is the resistivity = 1.68 * 10⁻⁸ Ω*m

L is the length

r is the radius = diameter/2 = 0.300mm/2 = 0.15 mm

Convert the radius to meters, where:

1 m = 1000 mm

0.15mm = 0.15 x 10⁻³ m

Now, input values into the formula and solve fo L:

`0.500=(1.68*10^(-8)* L)/(\pi*(0.15*10^(-3))^2)`

Solving further, rewrite the equation for the length L:

`\begin{gathered} L=(0.500\pi*(0.15*10^(-3))^2)/(1.68*10^(-8)) \\ \\ L=(3.534*10^(-8))/(1.68*10^(-8)) \\ \\ L=2.1\text{ m} \end{gathered}`

Therefore, the length of the copper wire is 2.1 meters.

ANSWER:

2.1 m