1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Discretization of RC-circuit

  1. Dec 9, 2016 #1
    1. The problem statement, all variables and given/known data

    Derive a discrete formula for an RC circuit for Vab[k] using the forward difference approximation. It should be of the form Vab[k + 1] = α Vab[k], and depend only on T, R, and C. For T = 0.076 s, R = 3 kΩ, and C = 10 mF, what is α?

    T is the period.
    The current is going from a to b.

    2. Relevant equations

    Ohms law
    Forward difference formula

    3. The attempt at a solution

    I cant find the equation editor...

    dVab(t)/dt = (1/c)I(t)


    dVab[k]/dt = I[k]/c

    which is approximately equal to

    (Vab[k+1] - Vab) / T

    solving for Vab[k+1]

    Vab[k+1] = (T/C)I[k] + Vab[k]

    From Ohm's law for a simple RC circuit we can find that

    I = Vab/R


    Vab[k+1] = (T/RC)Vab[k] + Vab[k]

    Vab[k+1] = ((T/RC)+1) Vab[k]

    it follows that

    α = (T/RC)+1)

    which yields a result of approximately 1.0025

    however, the solutions manual claims that the answer is 0.9975 which is (1-(T/RC))
  2. jcsd
  3. Dec 9, 2016 #2
    I think I solved it. I swapped
    (Vab[k+1] - Vab) / T

    (-Vab[k+1] + Vab) / T

    because of the orientation of the current.
  4. Dec 11, 2016 #3

    rude man

    User Avatar
    Homework Helper
    Gold Member

    There is only ONE RC circuit in the universe? How about showing us a schematic drawing ...
    The problem wording suggests that the output voltage is decaying in which case you know alpha has to be < 1.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted