1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Archived Sensitivity in potential divider circuits.

  1. Mar 13, 2009 #1
    1. The problem statement, all variables and given/known data
    Why is sensitivity in a potential divider circuit greatest when the resistance of the fixed resistor is equal to the average resistance of the other resistor (in my case a LDR)?

    This isn't a homework question, but I need to include a bit on why I chose the fixed resistor I did in my coursework - I know I chose it for the reason that it has the highest sensitivity, but I need to explain why this is.


    2. Relevant equations

    V2 = (R2 / (R1 + R2)) * V1


    3. The attempt at a solution

    ...I don't know >.>; help much appreciated.
     
  2. jcsd
  3. Feb 6, 2016 #2

    gneill

    User Avatar

    Staff: Mentor

    Suppose that we have a voltage divider with a fixed resistance ##R_f## and a sensor with an average resistance ##R## configured so that:

    ##\frac{V_{out}}{V_{in}} = \frac{R_f}{R_f +R}##

    We'll call the sensitivity ##S## of the divider the magnitude of amount by which the voltage ratio changes with respect to small changes in R. So:

    ##S = \left| \frac{d}{dR}\left( \frac{R_f}{R_f +R} \right) \right| = \frac{R_f}{(R_f + R)^2}##

    Now we'd like to maximize this sensitivity through a good choice of ##R_f##. Differentiating again and setting equal to zero:

    ##\frac{dS}{dR_f} = \frac{(R_f - R)}{(R_f + R)^3} = 0##

    We can see that it is zero when ##R_f = R##, making the average sensor resistance value ##R## the best choice for ##R_f##.

    Note that I didn't check to prove that what was found was a maxima rather than a minima; Left as an exercise for the student :smile:
     
    Last edited: Feb 6, 2016
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Sensitivity in potential divider circuits.
  1. Potential Divider (Replies: 2)

  2. Potential Divider (Replies: 3)

  3. Potential Divider (Replies: 2)

Loading...