- #1
Basher
- 13
- 0
Homework Statement
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.
Homework Equations
v(t) = 1/C ∫ i(t)dt +v(t0) {I realize their has to be limits for the integrand,I just can't type them}
A = [1/2.π.r^2]
The Attempt at a Solution
now after a while of thinking i realized 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?