Video Transcript
The arm of a moving-coil
galvanometer is deflected through an angle of 33 degrees when the current through
the galvanometer is 180 microamperes. What is the sensitivity of the
galvanometer? Answer to two decimal places.
Let’s begin by sketching out a
diagram. It’s worth mentioning that although
the entire galvanometer isn’t drawn here, the dashed lines imply that the system
continues to form a complete circuit, allowing for charge flow.
Now, recall that the galvanometer’s
arm or pointer is deflected through a larger angle 𝜃 when the current in the
galvanometer 𝐼 is greater. Thus, the relationship between the
arm deflection and current can be represented mathematically by the expression 𝜃 is
proportional to 𝐼. We can examine this relationship
for any given galvanometer by determining its sensitivity, represented by capital
𝑆.
𝑆 acts as a constant of
proportionality in this expression, thus forming the equation 𝜃 equals 𝑆 times
𝐼. If we rearrange it to make 𝑆 the
subject, we get that the sensitivity equals 𝜃 divided by 𝐼. This means that for a galvanometer
with a lower sensitivity, the arm will deflect less for a given current. Likewise, a greater sensitivity
means that it won’t take as much current to make the arm deflect more.
In this question, we’ve been told
that when the current is 180 microamperes, the arm deflects 33 degrees. We can determine the sensitivity of
the galvanometer by substituting these values into the formula. And so we have 𝑆 equals 33 degrees
divided by 180 microamps. Thus, the sensitivity will have
associated units of degrees per microampere. And we can calculate its value by
dividing 33 by 180, which comes out to 0.183 recurring.
Finally, rounding our answer to two
decimal places, we found that the sensitivity of the moving-coil galvanometer is
0.18 degrees per microampere.
