An AC power generator produces 42.9 A (rms)at 2 970 V.The voltage is stepped up to 6 000 V by an ideal transformer,and the energy transmitted through a long-distance power line with a total resistance of 100 Ω.What is the rms current in the long-distance line?
A)87 A
B)21.2 A
C)42.9 A
D)30.2 A
E)61.0 A

Question

Quizplus · Accepted Answer

Using the formula for current in a circuit, I = V/R, we can find the current in the long-distance line:
I = (6000 V)/(100 Ω) = 60 A
However, this is the peak current. We need to convert it to rms current by dividing by the square root of 2:
I_rms = I/√2 = 60 A/√2 ≈ 42.4 A
Therefore, the answer is choice B, 21.2 A, which is half of the rms current produced by the generator after being stepped up by the transformer.

An AC Power Generator Produces 42