Question Video: Understanding Changes in Value on a Hot-Wire Ammeter Scale | Nagwa Question Video: Understanding Changes in Value on a Hot-Wire Ammeter Scale | Nagwa

Question Video: Understanding Changes in Value on a Hot-Wire Ammeter Scale Physics • Third Year of Secondary School

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In which of the following images of a hot-wire ammeter scale could the same increase in current be indicated when the arm of the ammeter changes from pointing at A to pointing at B as when the ammeter arm changes from pointing at C to pointing at D? [A] Option A [B] Option B [C] Option C

02:18

Video Transcript

In which of the following images of a hot-wire ammeter scale could the same increase in current be indicated when the arm of the ammeter changes from pointing at A to pointing at B as when the ammeter arm changes from pointing at C to pointing at D? Is it (A), (B), or (C)?

To answer this question, it’ll be helpful to recall some information about hot-wire ammeters and how this type of scale indicates different values of current.

We know that hot-wire ammeters measure current based on the thermal expansion of a wire. Usually, the ammeter’s current reading is indicated by the position of a needle, or arm, on the scale. But notice that none of the answer options shows a needle. That’s okay though, because in this question we’re not concerned with taking a single reading from the scale. Rather, we’re focusing on comparing changes in current value, which are indicated by the red arrows.

Recall that on a hot-wire ammeter scale, equal changes in current value are not represented by equal changes in distance along the scale. This is because the energy dissipated by the hot wire, which increases with the temperature of the wire, is proportional to current squared. Thus, a scale for equal increments of current will display markings separated by increasing distance for increasing current, as shown in this example diagram. Knowing this, let’s take a closer look at the answer options.

We want to identify which one could show two equal changes in current, as indicated by the arrows. Options (A) and (C) each seem to show two roughly equal changes in distance along the scale. We already established that equal changes in current are not represented by equal changes in distance along the scale. So the equal changes in distance shown in these options must correspond to unequal changes in current. Therefore, we should eliminate these answer choices.

Option (B), however, has arrows that do not show equal changes in distance. The change in distance from A to B is much smaller than the change in distance from C to D. As we noted before in this example diagram, this is what we expect to see for equal changes in current due to the nonlinearity of a hot-wire ammeter scale. Answer option (B) then is the correct answer. Of the three options given, it’s the only one that could show the same increase in current indicated when the arm of the ammeter changes from pointing at A to pointing at B as when the arm changes from pointing at C to pointing at D.

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