A wire of length 10m of resistance .1 ohms per meter is used to supply power to the device. It is supplying 1A current @ 100 V 1 KHz AC to the device. What will be the power dissipation in the wire?
Well, the resistor would have a drop of 1V (V= len*sheet_resistance*Current = 10*0.1*1)across it. The current through that is 1A. If the current and voltage are given in terms of RMS, then you can multiply the rms voltage across the resistor and rms current to get the power dissipated.
Don't forget the return wire which will have the same dissipation if it is the same as the feed wire. The combined effect will be heat distributed over 1 meter.