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Question Video: 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 𝜇A. Which of the following must be true of the current 𝐼 that passes from contact A to contact B? [A] 𝐼 = 150 𝜇A [B] 𝐼 = −150 𝜇A [C] 𝐼 = 0 𝜇A [D] (150 > 𝐼 > 0) 𝜇A [E] (−150 < 𝐼 < 0) 𝜇A

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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 𝐼 that passes from contact A to contact B? (A) 𝐼 equals 150 microamperes. (B) 𝐼 equals negative 150 microamperes. (C) 𝐼 equals zero microamperes. (D) 150 is greater than 𝐼 is greater than zero microamperes. (E) Negative 150 is less than 𝐼 is less than zero microamperes.

Let’s begin by recalling that the galvanometer scale and arm, or pointer, indicate the current in the galvanometer coils. And here we know that when the current reaches a magnitude of 150 microamperes, so either positive or negative, the arm deflects to its maximum angle for reading on the scale. This feature is shown in the diagram, as the limiting values marked on the scale are positive 150 microamps and negative 150 microamps. Notice that zero lies exactly in between. And if the coils had no current in them, the arm would indicate zero microamperes. However, the arm is actually indicating a nonzero value. So, we know answer choice (C) is incorrect.

The arm is pointing to the left of the zero mark, indicating that there is a negative value of current. Also, it’s good to remember that the sign of the current differentiates the direction of charge flow, clockwise or counterclockwise, in the coils. Because the galvanometer is indicating a negative value, we know that the current 𝐼 can’t be positive 150 microamps, and it can’t be between zero and positive 150 microamps. So, let’s also eliminate options (A) and (D).

Now, option (B) suggests that the current is negative 150 microamps, which would mean that the arm has to be fully deflected over to the far-left side of the scale. This clearly isn’t the case since the arm is actually closer to the zero mark than full-scale deflection. So, we know (B) isn’t correct. So, we’re left with answer choice (E). And it does indeed agree with what we just noted that the current is negative somewhere between zero and negative 150 microamps.

Thus, negative 150 is less than 𝐼 is less than zero microamps does describe the current in the galvanometer. So, answer choice (E) is correct.

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