Posted by shaknocka lewis on .
A generating station is producing 1.2 x 106 W of power that is to be sent to a small town located 4.2 km away. Each of the two wires that comprise the transmission line has a resistance per length of 5.0 x 10-2/km. (a) Find the power lost in heating the wires if the power is transmitted at 1200 V. (b) A 100:1 step-up transformer is used to raise the voltage before the power is transmitted. How much power is now lost in heating the wires?
The total resistance of the wires is Rwire = 4.2*0.05 = 0.21 ohms.
The current flowing in the wires when delivering 1.2*10^6 W is P/V
= 1.2*10^6 W/1200 = 1000 A
Poower lost in wires
= I^2*Rwire = 210,000 W
With a 100:1 stepup transformer, I is 100 x less. The power is delivered the same but the loss in the wires is 10^4 times less, or 21 W