How do I calculate the resistance of a copper bar?
While you can look up the resistivity of copper on wikipedia or Kaye &amp; Laby, you'll find that the answer is given in units of 10^-8/m. I don't know about you, but I always miscount powers of 10 when using that sort of unit. Instead I commit the following to memory

1 metre of \$1mm^2\$ copper wire has a resistance of 17 \$m\Omega\$ (roughly)

If you can't remember that resistance is proportional to length, and inversely proportional to area, then just think series resistors, or parallel resistors. 

10m of wire would have 10x the resistance, it's like ten 1m lengths in series.

If the wire is 4mm2, it will have 1/4 the resistance, because it's like four 1m lengths in parallel.

Copper, like all pure metals, has a fairly strong temperature coefficient of resistance, which is why I've only given the resistivity to 2 significant figures. The tempco is 0.4% per degree C, or a whopping 10% change for 25 degree change in temperature. It can be useful to remember that when you want to estimate the temperature rise of (say) transformer windings, just measure their resistance cold, and again when hot.