# Finding expression for the current

1. Mar 5, 2017

### Ahmed Hassona

< Mentor Note -- thread moved to HH from the technical forums, so no HH Template is shown >

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

Last edited by a moderator: Mar 5, 2017
2. Mar 5, 2017

### Staff: Mentor

Welcome to the PF. I've moved your thread to the schoolwork forums, where it fits better than in the EE forum.

This equation "V(t) = Ri(t) + V_out (t)" looks wrong to me. There is the voltage source, the voltage across the capacitor, and Vout which is I*R. Do you want to take another cut at the equations? Or am I just misreading them?

3. Mar 5, 2017

### Ahmed Hassona

It's the first time I work with electrecity so I am sure that you are right about this eqn "V(t) = Ri(t) + V_out (t)" is wrong. But then how can I substitute V(t) with V_out (t) in the i(t) eqn. ?

4. Mar 5, 2017

### Staff: Mentor

So you are basically writing a "loop" equation for the circuit. Have you learned Kirchoff's Voltage Law yet? It says that the sum of all voltages around a closed loop circuit will be zero. So call the voltage source on the left Vs, the voltage across the capacitor Vc, and the voltage across the resistor Vout. Add the voltages as you go around the loop clockwise, from the bottom node, all the way back around to the bottom node.

Since you see the - terminal of the voltage source first, and you are travelling from - to + on the part, you call that voltage a positive gain. Since you go across the capacitor and resistor from + to -, you call that a negative voltage gain (or a voltage drop).

So you would write an equation like this:

+Vs - Vc - Vout = 0

Then substitute the equations you wrote for the Vc and Vout, and solve the resulting equation. Does that help?

Last edited: Mar 5, 2017
5. Mar 5, 2017

### Ahmed Hassona

Yeah it helped me alot. Thank you so much, really appreciate it