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: Capacitance - finding the voltage across a capacitor given a time varying current

  1. Jul 11, 2012 #1
    1. The problem statement, all variables and given/known data


    referring to the attatchment. the current consists of two semi circles. the question asks me to find the voltage across a 47-uF capacitor when t = 2ms.

    2. Relevant equations

    v(t) = 1/C ∫ i(t)dt +v(t0) {I realise their has to be limits for the integrand,I just can't type them}

    A = [1/2.π.r^2]

    3. The attempt at a solution
    now after a while of thinking i realised i could find the area under the curve of this circle with the area formula multiplied by the capacitnce which gives me the right answer.

    However, in my first attempt i assigned an equation to the first semi circle. this was

    (2√(1 - (t - 1)^2))

    then i integrated this by using trigonometric substitution.

    I came up with this

    arcsin(t - 1) + (t - 1)*(√(1 - (t - 1)^2))

    i then evaluated at the upper limit t giving me the same formula.

    then evaluated at t0 = 0 giving (-π/2). i then subtracted this away from the top formula.

    so my entire formula is arcsin(t - 1) + (t - 1)*(√(1 - (t - 1)^2)) + (π/2).

    substituting t = 2ms i'm left with (π/2) + (π/2) = π.

    i multiply by 10^-6 because i have to account for the axes being both in ms and mA.

    then i divide by 47-μF giving me double the correct answer. roughly 66.48mV. however the answer is half that. where did is screw up with the integral evaluation???
  2. jcsd
  3. Jul 11, 2012 #2


    User Avatar
    Science Advisor
    Homework Helper

    Hi Basher! :smile:

    (try using the X2 button just above the Reply box :wink:)
    nooo … √(4 - (t - 1)2)) :wink:
  4. Jul 11, 2012 #3
    thanks. Did you have a crack at the problem?
  5. Jul 12, 2012 #4


    User Avatar
    Science Advisor
    Homework Helper

    or a bash? :wink:

    no … i was perfectly happy with …
  6. Jul 12, 2012 #5
    hahaha. fair call. thanks
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook