Question

The resistance of a uniform copper wire 50.0 meters long and 1.15mm in diameter is 0.830 ohms at 20°C. What is the resistivity if the copper at this temperature?

Answer 1

The resistance of the copper wire is:

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

where $\rho$ - the resistivity of the copper;

l - the lenght of the wire;

S - the cross-sectional area of the wire;

d - the diameter of the wire.

So, resistivity is:

$\rho=\frac{\pi d^2R}{4l}=\frac{3.14\cdot 0.00115^2\cdot 0.83}{4\cdot 50}=1.72\cdot 10^{-8}\space Ohm\cdot m.$