Answer
a. 8.33 A.
b. 83.3 V.
c. 1.38 kW.
d. Stepping up voltage reduces the fraction of power lost.
Work Step by Step
a.
$$Electric \; power = (current) \times (voltage)$$
$$100,000 W = (I)(12000 V)$$
So I = 8.33 A.
b. By Ohm's Law, $V = IR = (8.33 A)(10 \Omega) = 83.3 V$ voltage drop along each power line.
c. In each line, $Electric \; power = (current) \times (voltage) = (8.3 A)(83.3 V) = 691 W$. In both lines, the total power wasted/dissipated as heat 2(691 W) = 1.38 kW.
d. In this example, the 1.38 kW lost as heat is a few percent of the transmitted power. If the transmission voltage were 5 times lower, 2400 V, the current would be 5 times more, and the lost heat would be 25 times more! High-voltage power transmission is relatively efficient.
