How Is Minimum Sensitivity Calculated in Instruments?

[Precursor]

Homework Statement

The attempt at a solution
First, we define sensitivity as the change of an instrument or transducer's output per unit change in the measured quantity.

So to find the minimum sensitivity I simply plugged in the largest possible input (5.0 mm) into the equation:

E = 9.5e^-0.4(5.0)

E = 1.286 V

Is this correct?

 

[lanedance]

I would say no, that is in fact the "minimum voltage" you would expect to occur

I would associate sensitivity with rate of change of voltage with distance

 

[Precursor]

So I would first have to take the derivative, and then plug in 5.0?

Doing this I would get an answer of -0.514 V/mm. So will my final answer be 0.514 V/mm, if I were to take the absolute value?

 

[lanedance]

if you can explain why you choose 5 (which is a reasonable choice), it sounds like a plan

 

[Precursor]

I chose a displacement of 5.0 mm because it will give me the smallest rate of change, whereas if I chose a number closer to 0, I would get a higher rate of change, which means higher sensitivity.

Also, do I keep the value negative, or take the absolute value? I don't think negative sensitivity makes sense.

 

[lanedance]

may have to check you notes, it may be defined as the magnitude of rate of change as you're hinting