Question

An experiment was performed to determine the efficiency of a transformer. A coil is placed into another coil, and a steel bar is placed on the inside of both coils.

f (efficiency) = V1*N2 / V2*N1

Suppose we ignore the possibility of someone having miscounted the number of turns. Why might "1 turn" (or, perhaps, "1/2 turn") still make sense as an uncertainty on the number of turns?

Answer 1

Let us consider an equivalent situation. Suppose you are trying to measure the distance using a common meter scale. Your measurement records distance 4.5cm. Last digit 5 is the least significant digit. In your measurement effort, 4.5 cm mark was close to the end point of the distance and it was not exactly on the end point. In other words, it was the closest mark to the end point of distance, therefore we accepted it 4.5 cm. The point is that the last digit 5 is not certain but doubtful because of the fact that the resolution of measuring instrument is not beyond 0.1 cm or 1mm. Similar argument holds in the case of number of turns. In an experiment where the number of turns need to be counted, the last digit of the number is taken to be uncertain by 1, that is, if you counted the number of turns to 125 then last digit 5 is the least significant digit and doubtful. In other words, your counting count like 1,2,3 etc and not 1.1, 1.5 etc.

Hope this helps.