(adsbygoogle = window.adsbygoogle || []).push({}); 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???

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

**Physics Forums | Science Articles, Homework Help, Discussion**