A dopey resistance question.

  1. Dadface

    Dadface 2,069
    Gold Member

    You have a length of bare resistance wire a fixed contact and a sliding contact.Using these things only how can you make a variable resistor such that when the sliding contact is moved along the wire the resistance varies smoothly from zero to a maximum and then to zero?You are not allowed to cut the wire.
     
  2. jcsd
  3. Gokul43201

    Gokul43201 11,141
    Staff Emeritus
    Science Advisor
    Gold Member

    Form the wire (of length L and resistance R) into a closed loop. If the sliding contact is at a distance d from the fixed contact, the resistance will be the equivalent parallel resistance from segments of length d and L-d, which should be:

    R_eff = [R(d/L)*R((L-d)/L)]/[R(d/L)+R((L-d)/L)] = Rd(L-d)/(L^2),

    and as d increases from 0, d(L-d) increases smoothly from 0 till d=L/2 (where R_eff is at its maximal value of R/4) and decreases smoothly to 0 after that (this part maps onto the common puzzle of maximizing the area of a rectangle of given perimeter, but if you don't like that, then the first derivative is L-2d, and the second is -2).
     
  4. Dadface

    Dadface 2,069
    Gold Member

    Well done Gokul 43201.
     
Know someone interested in this topic? Share a link to this question via email, Google+, Twitter, or Facebook

Have something to add?
Similar discussions for: A dopey resistance question.
Loading...