Can someone please help me on this problem
C1 is initially charged to 1 volt.
The switch closes at t=0. Find and plot all the currents.
Since the switch is initially i assume all initial conditions are:
i1(0) = i2(0) = i3(0) = i4(0) = i5(0) = 0
so I write a KVL loop equation for each loop and get :
' - denotes derivative
int - denotes integral
Loop 1 : [1/c1 * int(i1*dt) + 1] + L1*i1' + R1*i2 = 0
==> L1*i1'' + R1i2' + i1/c1 = -1
Loop 2: R1*i2 + 1/c2 *int(i3*dt) + R2*i3 + L2*i4' = 0
==> L2*i4'' + R2*i3' + R1*i2' +i3/c2 = 0
Loop 3: L2*i4' = R3*i5
KCL equations give:
i1 = i2 + i3
i3 = i4 + i5
I solved for i1''(from loop1 equation) and i4''(from loop 2 equation).
I'm kind of stuck at this point. I don't know how to setup the equations from here so that they can be solved. I tried solving for the first derivatives but that didn't really give me anything.
Does anyone have any suggestions or tips?