The voltage across a 0.18 micro Farad capacitor is: v=40v for t <= 0 v= Ate^(-5000t)+Be^(-5000t) for t>=0 The current in the capacitor at t=0+ is 152 milliamperes. Assume passive sign convention. 1. Find initial energy stored in capacitor. For this i used w=.5cv^2=.5(.00000018)(40^2)= 144microJules 2. Find the coefficient A in v/s. I don't know how to get this one 3. Find the coefficient B. I used the equation for t>=0 and put 40 in for v and 0 in for t and solved and got B=40v 4. Find the current in the capacitor when t=2.76 milliseconds. I believe i need to figure out number 2 before I can do this one. Can I get some reassurance on 1 and 3 and some help on 2 and 4
You should be able to make use of the differential relationship Ic(t)=CdVc(t)/dt Where Ic(t) is the capacitor current with respect to time and Vc(t) is the stated capacitor voltage relationship wrt time. So differentiate the voltage relationship and make use of the stated initial conditions at t=0+ by plugging them into the derived current function. Given you have B you should then find A.
I think you should solve 3 and get B before you do 2. It looks like if you take the point t=0- you know Vc and t so should be able to find B. Try that and then use tnk's advice for solving 2.
You were getting there but must have missed something. Always helps if you post your working as you go. I've attached my solution - hopefully it's correct. You may want to delay looking at the pdf and retry your solution. I get A=1.0444x10^5 and i(2.76ms)=-0.281uA