# Homework Help: Integration and RC Step response

1. Feb 22, 2010

### 0tt0UK

Integration

1. The problem statement, all variables and given/known data

Hi everyone,

I'm new here. This is my first post. I found physicsforums when researching on google a solution for a doubt I've had when trying to solve rc step response. Basically, the RC analyse showed at http://freespace.virgin.net/ljmayes.mal/circuittheory/Rcstep.htm" solves step by step the mathematical behave of RC circuits.

I understand the whole anylise but the line with the follow part (integrating):

2. Relevant equations

$$\int$$dt = RC$$\int$$$$\frac{1}{Vin - Vc}$$dVc

t = - CR ln(Vin - Vc) + const

Last edited by a moderator: Apr 24, 2017
2. Feb 22, 2010

### Staff: Mentor

Yes, that's correct (or at least close. The right side should be ln |x| + const.

Similarly,
$$\int\frac{du}{u}~=~ln|u| + C$$

Using an ordinary substitution in your problem, u = Vin - VC, what will du be?

Last edited by a moderator: Apr 24, 2017
3. Feb 22, 2010

### 0tt0UK

du in function of Vc ?

du = -1 ? is that right?

4. Feb 22, 2010

### Staff: Mentor

No, if u = Vin - VC, then du = -dVC.

5. Feb 22, 2010

### 0tt0UK

right!? so how would you solve

$$\int$$$$\frac{1}{Vin - Vc}$$dVc ??

Would you differentiate 1/Vin-Vc in function of Vc and then integrate the result?

sorry I still don't understand the "-" on the right side of the eq.

thanks

6. Feb 22, 2010

### Staff: Mentor

Use and ordinary substitution with u = Vin - VC.

What is du?
Make the substitution and do the integration. What do you get?

7. Feb 22, 2010

### 0tt0UK

- ln (Vin - Vc) + const
thanks very much Mark44

Last edited: Feb 22, 2010