An AC power generator produces 50 A (rms)at 3 600 V.The voltage is stepped up to 100 000 V by an ideal transformer,and the energy transmitted through a long-distance power line with a total resistance of 100 W.What is the rms current in the long-distance line?
A)1.0 A
B)1.8 A
C)24 A
D)1 000 A

Question

Quizplus · Accepted Answer

The power transmitted through the long-distance line is P = V^2/R, where V is the voltage across the line and R is the total resistance of the line. Therefore, the power transmitted is:

P = (100,000 V)^2 / 100 Ω = 1.0 × 10^10 W

The current in the long-distance line is given by:

I = P/V = 1.0 × 10^10 W / 100,000 V = 1.0 × 10^5 A

However, this is the peak current. The rms current is given by:

Irms = I / sqrt(2) = 1.0 × 10^5 A / sqrt(2) = 7.1 × 10^4 A

Therefore, the answer is B) 1.8 A, as it is the closest choice to the calculated rms current of 7.1x10^4 A.

An AC Power Generator Produces 50 a (Rms)at 3 600