Question Video: Determining Whether Hot Wire Ammeters Use Non-Linear Scales | Nagwa Question Video: Determining Whether Hot Wire Ammeters Use Non-Linear Scales | Nagwa

Question Video: Determining Whether Hot Wire Ammeters Use Non-Linear Scales Physics • Third Year of Secondary School

In the following image of a hot-wire ammeter scale, is the increase in current indicated when the arm of the ammeter changes from pointing at 𝐴 to pointing at 𝐡 equal to the increase in current indicated when the arm of the ammeter changes from pointing at 𝐡 to pointing at 𝐢? The length of the arrow from 𝐴 to 𝐡 equals the length of the arrow from 𝐡 to 𝐢.

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Video Transcript

In the following image of a hot-wire ammeter scale is the increase in current indicated when the arm of the ammeter changes from pointing at 𝐴 to pointing at 𝐡 equal to the increase in current indicated when the arm of the ammeter changes from pointing at 𝐡 to pointing at 𝐢? The length of the arrow from 𝐴 to 𝐡 equals the length of the arrow from 𝐡 to 𝐢.

Let’s recall that hot-wire ammeter scales are nonlinear, which means when reading a dial of a hot-wire ammeter to get a value of current, equal changes in distance will indicate nonequal changes in the value of current. Because the relationship between the current and how far this arm moves is nonlinear. And specifically, the movement of the dial arm is proportional to the square of current. This means that the arm has to move through a larger and larger distance for the same increase in current each time.

So because the question tells us that the length of the arrow from 𝐴 to 𝐡 equals the length of the arrow from 𝐡 to 𝐢 and 𝐡 to 𝐢 is further along in the hot-wire ammeter scale, it must mean that the distance between 𝐴 and 𝐡 is indicating a larger change in current than the distance from 𝐡 to 𝐢, which means no, the increase in current between the two different distances is not the same.

But why is this? Most other ammeters don’t have this strange nonlinear scale? Well, the answer has to do with the β€œhot” part of this hot-wire ammeter. When there is a current through the hot wire, the movement of electric charge causes the hot wire to heat up. We represent this heat with the variable 𝑄. And it turns out that this produced heat is proportional to the square of the current going through that hot wire.

This means if you were to double the current, you would increase the heat in the wire by four times or quadruple it. And all of the mechanisms in a hot-wire ammeter β€” the pulley, the spring, the string, and the hot wire itself β€” are using the expansion of the metal of this hot wire, which occurs when it heats up in order to produce a movement in the dial arm, which essentially means that this arm movement is proportional to the heat in the hot wire 𝑄, which is why the arm movement is thus proportional to the square of the current through the wire.

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