+0

# What diameter should you make a copper wire so its resistance is 0.015 Ω per meter of length?

0
313
1
What diameter should you make a copper wire so its resistance is 0.015 Ω per meter of length?
physics
Guest Feb 25, 2015

#1
+18829
+5

What diameter should you make a copper wire so its resistance is 0.015 $$\Omega$$ per meter of length ?

The resistance R of a copper wire with the length l can be calculated with the following formula:

where

R = resistance (ohms, Ω)

ρ = resistivity (ohm meter, Ω m)  Resistivity Copper: 1.7 x 10-8 Ω m

l = length of conductor (m)

A = cross-sectional area of conductor (m2)

d  = the nominal diameter of the wire

We have:

$$\frac{R}{l}= 0.015\ \frac{\Omega}{m}$$

$$\boxed{\dfrac{R}{l}= \dfrac{4\cdot \rho}{\pi \cdot d^2}} = 0.015\ \frac{\Omega}{m}\\\\ \dfrac{4\cdot \rho}{\pi \cdot d^2}} = 0.015\ \frac{\Omega}{m}\\\\ d^2 = \dfrac{4\cdot \rho}{\pi \cdot0.015\ \frac{\Omega}{m}}} \quad | \quad \rho_{copper} = 1.7 \cdot 10^{-8}\ \Omega\ m\\\\\\ d^2 = \dfrac{4\cdot 1.7 \cdot 10^{-8}\ \Omega\ m}{\pi \cdot0.015\ \frac{\Omega}{m}}} \quad | \quad \sqrt{} \\\\\\ d = 2 \cdot 10^{-4} \sqrt{ \dfrac{1.7}{\pi\cdot 0.015} }\ m \\\\ d = 0.00120125135\ \mathrm{m} \\ d = 1.2\ \mathrm{mm}$$

heureka  Feb 25, 2015
Sort:

#1
+18829
+5

What diameter should you make a copper wire so its resistance is 0.015 $$\Omega$$ per meter of length ?

The resistance R of a copper wire with the length l can be calculated with the following formula:

where

R = resistance (ohms, Ω)

ρ = resistivity (ohm meter, Ω m)  Resistivity Copper: 1.7 x 10-8 Ω m

l = length of conductor (m)

A = cross-sectional area of conductor (m2)

d  = the nominal diameter of the wire

We have:

$$\frac{R}{l}= 0.015\ \frac{\Omega}{m}$$

$$\boxed{\dfrac{R}{l}= \dfrac{4\cdot \rho}{\pi \cdot d^2}} = 0.015\ \frac{\Omega}{m}\\\\ \dfrac{4\cdot \rho}{\pi \cdot d^2}} = 0.015\ \frac{\Omega}{m}\\\\ d^2 = \dfrac{4\cdot \rho}{\pi \cdot0.015\ \frac{\Omega}{m}}} \quad | \quad \rho_{copper} = 1.7 \cdot 10^{-8}\ \Omega\ m\\\\\\ d^2 = \dfrac{4\cdot 1.7 \cdot 10^{-8}\ \Omega\ m}{\pi \cdot0.015\ \frac{\Omega}{m}}} \quad | \quad \sqrt{} \\\\\\ d = 2 \cdot 10^{-4} \sqrt{ \dfrac{1.7}{\pi\cdot 0.015} }\ m \\\\ d = 0.00120125135\ \mathrm{m} \\ d = 1.2\ \mathrm{mm}$$

heureka  Feb 25, 2015

### 7 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details