Question Video: Determining the Effect of Increasing the Sensitivity of a Moving-Coil Galvanometer | Nagwa Question Video: Determining the Effect of Increasing the Sensitivity of a Moving-Coil Galvanometer | Nagwa

Question Video: Determining the Effect of Increasing the Sensitivity of a Moving-Coil Galvanometer Physics • Third Year of Secondary School

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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.

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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.

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