Video Transcript
Which of the following best
describes an advantage of increasing the sensitivity of a moving-coil
galvanometer? (A) It increases the resolution of
the galvanometer. (B) It increases the maximum
current measurable by the galvanometer.
This question is asking us about
the sensitivity of a moving-coil galvanometer. Specifically, we need to identify
the best description of the advantage gained from increasing the sensitivity. Let’s recall that a moving-coil
galvanometer has a display with a needle that deflects through an angle, 𝜃, in
response to a current, 𝐼, through it. The amount that the needle deflects
indicates the current through the device. And in this way, a moving-coil
galvanometer can be used to measure a current.
Let’s now recall how the
sensitivity of a moving-coil galvanometer is defined. The sensitivity, 𝑆, is equal to
the deflection angle, 𝜃, divided by the current, 𝐼. That is, the sensitivity tells us
how much the needle deflects by for a given current through the galvanometer. Increasing the sensitivity, 𝑆,
means increasing the value of 𝜃 for a given value of 𝐼. In other words, for a given value
of current through the device, the needle in a galvanometer with a greater
sensitivity will deflect through a larger angle.
Now there must be some smallest
deflection angle that we are capable of reading clearly from a galvanometer
display. Let’s label this smallest
deflection angle we can read as 𝜃 min. In practice, this may correspond to
the smallest increment marked on the galvanometer scale and would likely be of the
order of a few degrees. Let’s now imagine we have a
galvanometer with a sensitivity 𝑆 such that the smallest readable deflection angle
corresponds to a measured current 𝐼 min. This current 𝐼 min is the smallest
current that we can accurately measure using this particular galvanometer. The smaller this minimum readable
current, the greater the resolution of the galvanometer.
Now let’s suppose we have a second
galvanometer with twice the sensitivity of the first. Replacing 𝑆 by two 𝑆, we see that
the right-hand side of the sensitivity equation for the minimum measurable current
becomes two multiplied by 𝜃 min over 𝐼 min. We can rewrite this as 𝜃 min
divided by a half times 𝐼 min. This new way of writing the
equation is helpful because it tells us that for a given minimum readable deflection
angle 𝜃 min, doubling the sensitivity means halving the minimum current that can be
measured. We know that a smaller value of
this minimum current means a greater resolution. So, we have found that increasing
the sensitivity means increasing the resolution. This is the statement given in
option (A).
Considering for a moment the
statement in option (B) that increasing the sensitivity means increasing the maximum
current the galvanometer can measure, we see that this is not true. The sensitivity is the ratio of the
deflection angle to the current. Increasing the sensitivity does not
increase the maximum measurable current.
Our answer then is that the correct
statement is the one in option (A). The advantage of increasing the
sensitivity of a galvanometer is that it increases the resolution of the
galvanometer.
