Question Video: Understanding the Current in a Moving-Coil Galvanometer Physics

The diagram shows a moving-coil galvanometer. Full-scale deflection of the galvanometer arm occurs when the galvanometer coils carry a current with a magnitude of 150 ๐œ‡A. Which of the following must be true of the current ๐ผ that passes from contact ๐ด to contact ๐ต? [A] ๐ผ = โˆ’150 ๐œ‡A [B] ๐ผ = 150 ๐œ‡A [C] ๐ผ = 0 ๐œ‡A [D] (150 > ๐ผ > 0) ๐œ‡A [E] (โˆ’150 < ๐ผ < 0) ๐œ‡A

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Video Transcript

The diagram shows a moving-coil galvanometer. Full-scale deflection of the galvanometer arm occurs when the galvanometer coils carry a current with a magnitude of 150 microamperes. Which of the following must be true of the current ๐ผ that passes from contact ๐ด to contact ๐ต? (A) ๐ผ equals negative 150 microamperes. (B) ๐ผ equals 150 micro amperes. (C) ๐ผ equals zero microamperes. (D) 150 is greater than ๐ผ is greater than zero microamperes. (E) Negative 150 is greater than ๐ผ is greater than zero microamperes.

To begin, letโ€™s recall that the purpose of a moving-coil galvanometer is to detect and indicate electric current. Itโ€™s the scale and arm or pointer up here that tell the user the magnitude and sign or direction of current in its coils. In this question, weโ€™ve been told that when the current reaches a magnitude of 150 microamperes, the arm deflects to its maximum angle for reading on the scale. This feature can be seen in the diagram, as the limiting values marked on the scale are negative 150 microamps and positive 150 microamps.

Since the scale is able to indicate an equal magnitude for both positive and negative values, we see that zero lies exactly in the middle. So if the coils had no current in them, the arm would indicate zero microamperes. But we can see that that isnโ€™t the case here because the arm isnโ€™t aligned with the zero mark. This means thereโ€™s a nonzero value of current in the coils, and we should eliminate answer choice (C).

Still the arm is closer to zero than either extreme value, positive or negative 150 microamps. Although those values are clearly marked on the scale, the arm isnโ€™t pointing to either. So we know answer choices (A) and (B) are wrong as well.

The two remaining answer choices basically just suggest that the current in the coils is either positive or negative. Remember that the sign of the current is indicated on the scale with either a plus or minus sign on either side of the zero mark. So these values to the left of the zero mark are negative, all the way down to negative 150 microamps. But clearly the pointer arm isnโ€™t in this region, so the value of current is not negative. And we can eliminate option (E).

Therefore, option (D) is looking pretty good. And just to confirm, we can practice reading the current from the scale. The arm is pointing to the second mark in the positive region of the scale, where there are 10 marks up to 150 microamps. Thus, each mark denotes 15 microamperes, so it looks like the arm is indicating a value of about positive 30 microamperes. This does lie within the range given by answer choice (D), 150 is greater than ๐ผ is greater than zero microamperes. Therefore, (D) is the correct answer.

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