Hi all,
I'm trying to find an expression for the current i(t) as a function of C and V_out (t) after t = 0. I have an answer but still not sure at all if its correct or not.
Here is my answer:
I know that
i(t) = C*dV(t) / dt
V(t) = Ri(t) + V_out (t)

combining them together

i(t) = C-dV_out(t)/dt - dV_out(t) / R

Here is the circuit.




Thanks

 

You have an error.
V(t) = Ri(t) + V_out (t) is wrong.

The correct equation is:
V(t)=Vresistor + Vcapacitor
V(t)=Vout(t) + Vcapacitor
V(t)=R*i(t) + Vcapacitor

I also not sure that i(t) = C*dV(t) / dt is correct.

 

You have an error.
V(t) = Ri(t) + V_out (t) is wrong.

The correct equation is:
V(t)=Vresistor + Vcapacitor
V(t)=Vout(t) + Vcapacitor
V(t)=R*i(t) + Vcapacitor

I also not sure that i(t) = C*dV(t) / dt is correct.

Yeah I just found out that V(t) = Ri(t) + V_out (t) is wrong.
I'm sure that i(t) = C*dV(t) / dt is correct because it is written in my lecture notes.
so from your equations, the expression for i(t) will be Cd(Vout(t) +Vc)/dt.
but what is the expression for Vc?
Sorry for my noob questions, it is my first time to work with circuits.

 

My issue with i(t) equation is that you show that voltage source V(t) is across the capacitor. That is not correct, as far as I see it. The voltage across capacitor is V(t)-Vresistor=V(t)-R*i(t).

Recall that sum of voltages in the circuit is zero. V(t) is the source, therefore: V(t)=Vcapacitor+Vresistor.
Which means that Vcapacitor=V(t)-Vresistor.
Then.
\(
i(t)=C\frac{d}{dt}[V(t)-V_{resistor}]
\)

Since you don't show the initial conditions of the circuit, it is really impossible to setup the capacitor equation correctly.