## RC circuit differential equations

Hi everyone...

I need to solve the differential equations of a RC circuit given a voltage and a current pulse. I have to get this responses:

I'm using matlab, with runge kutta. I've been solving the equations separately changing the initial conditions and the value of current and voltage, but i want to know if there is a way to get the response solving the differential equations only once??

By the way, the differential equations i'm trying to solve are

$$\frac{dV}{dt}=\frac{1}{C}(i(t)-\frac{V}{R})$$

and

$$I = \frac{dQ}{dt}=\frac{1}{R}(V-\frac{Q(t)}{C})$$

How should i solve this equations in order to get the responses showed in the pictures???

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 Do you know how to use Laplace transform to solve differential questions?
 Hi everybody, i'm trying to solve the equation: $$I(t) = \frac{dQ}{dt}=\frac{Q(t)}{CR}-\frac{V}{R}$$ in order to get this graph (V changes to simulate the pulse) I'm not getting this response, and i've checked my program (runge kutta) with a current pulse and works ok... So the only way i'm not getting what i want is that the differential equation i'm solving is wrong. Please, can you tell me the correct equation?? Thanks!!

## RC circuit differential equations

 Quote by gjfelix2001 Hi everybody, i'm trying to solve the equation: $$I(t) = \frac{dQ}{dt}=\frac{Q(t)}{CR}-\frac{V}{R}$$ in order to get this graph (V changes to simulate the pulse) I'm not getting this response, and i've checked my program (runge kutta) with a current pulse and works ok... So the only way i'm not getting what i want is that the differential equation i'm solving is wrong. Please, can you tell me the correct equation?? Thanks!!
If you drew the circuit you cared about I think we could help. Trying to "reverse engineer" what you are really interested in is a lot to ask!

jason

jason

 Tags circuit rc, kutta, ode, pulse, rc circuit