# Finding the expression for the current

#### Ahmed Karim

Joined Mar 5, 2017
2
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.
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

#### shteii01

Joined Feb 19, 2010
4,647
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.

#### Ahmed Karim

Joined Mar 5, 2017
2
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.

#### shteii01

Joined Feb 19, 2010
4,647
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.

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