Two cities are $$150\,km$$  apart. Electric power is sent from one city to another city through copper wires. The fall of potential per $$km$$  is $$8$$ volt and the average resistance per $$km$$  is $$0.5\,\Omega .$$  The power loss in the wires is :

Solution :
Total resistance $$R = \left( {0.5\,\Omega /km} \right) \times \left( {150\,km} \right) = 75\,\Omega $$
Total voltage drop $$ = \left( {8\,V/km} \right) \times \left( {150\,km} \right) = 1200\,V$$
Power loss $$ = \frac{{{{\left( {\Delta V} \right)}^2}}}{R} = \frac{{{{\left( {1200} \right)}^2}}}{{75}}W$$
$$\eqalign{ & = 19200\,W \cr & = 19.2\,kW \cr} $$