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.
