Question

A 546kW power station delivers power to a factory. The power is delivered through wires with a total (i.e. round-trip) resistance of 3.74Ohm. How much less power is wasted in the transmission wires if the electricity is delivered from the power station at 45000V rather than 12700V? (Hint: Consider the power plant as a battery delivering the voltage for the transmission line. How much current is flowing through the wire?)

Answer 1

Here ,

Power = Current * Voltage

545*10^3 = I*12700

I = 42.91 A

Now ,

Power wasted = I^2 * R

Power wasted = 42.91^2 * 3.74

Power wasted = 6887.5 W

Power wasted is 6887.5 W

Now , if Voltage is 45000 V

Power = Current * Voltage

545*10^3 = I*45000

I = 12.11 A

Now ,

Power wasted = I^2 * R

Power wasted = 12.11^2 * 3.74

Power wasted = 548.6 W

Power wasted is 548.6 W

difference in power loss = 6887.5 - 548.6

difference in power loss =6338.9 W

6338.9 W less power is wasted