RC circuit differential equations

In summary, Jason is trying to solve the differential equation of a RC circuit given a voltage and current pulse. He has been solving the equations separately changing the initial conditions and the value of current and voltage, but he wants to know if there is a way to get the response solving the differential equations only once. If you drew the circuit you cared about I think we could help.
  • #1
gjfelix2001
19
0
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:

http://i.imagehost.org/view/0340/Respuesta1 [Broken]

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

[tex]\frac{dV}{dt}=\frac{1}{C}(i(t)-\frac{V}{R})[/tex]

and

[tex]I = \frac{dQ}{dt}=\frac{1}{R}(V-\frac{Q(t)}{C}) [/tex]

How should i solve this equations in order to get the responses showed in the pictures?
 
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  • #2
Do you know how to use Laplace transform to solve differential questions?
 
  • #3
RC circuit: is this the right equation?

Hi everybody, I'm trying to solve the equation:

[tex]I(t) = \frac{dQ}{dt}=\frac{Q(t)}{CR}-\frac{V}{R}[/tex]

in order to get this graph (V changes to simulate the pulse)

[PLAIN]http://i.imagehost.org/0340/Respuesta1.jpg [Broken]

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!
 
Last edited by a moderator:
  • #4


gjfelix2001 said:
Hi everybody, I'm trying to solve the equation:

[tex]I(t) = \frac{dQ}{dt}=\frac{Q(t)}{CR}-\frac{V}{R}[/tex]

in order to get this graph (V changes to simulate the pulse)

[PLAIN]http://i.imagehost.org/0340/Respuesta1.jpg [Broken]

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
 
Last edited by a moderator:
  • #5


Hello! Solving the differential equations of an RC circuit can be a complex task, but it is definitely achievable with the right tools and approach. Using MATLAB and the Runge-Kutta method is a good start, but there are also other numerical methods that can be used, such as the Euler method or the fourth-order Runge-Kutta method.

To solve the equations and obtain the responses shown in the pictures, you will need to set up a system of equations that includes both the voltage and current equations. This can be done by treating the voltage and current as dependent variables and the time as the independent variable. You can then use a numerical solver, such as the one provided by MATLAB, to solve the equations simultaneously and obtain the desired response.

Additionally, you will need to specify the initial conditions for both the voltage and current, as well as the values of the resistance and capacitance in the circuit. This will allow the solver to accurately simulate the behavior of the RC circuit over time.

In summary, to solve the differential equations of an RC circuit and obtain the desired response, you will need to set up a system of equations, use a numerical solver, and specify the necessary initial conditions and circuit parameters. I hope this helps and good luck with your project!
 

1. What is an RC circuit?

An RC circuit is a type of electrical circuit that consists of a resistor (R) and a capacitor (C) connected in series or parallel. It is commonly used in electronic devices to control the flow of electric current.

2. What are differential equations in the context of RC circuits?

Differential equations in RC circuits are mathematical equations that describe the relationship between the voltage and current in the circuit. They take into account the properties of the resistor and capacitor, as well as the voltage source.

3. How are differential equations used in analyzing RC circuits?

Differential equations are used to analyze RC circuits by determining the behavior of the circuit over time. They can be used to calculate the voltage and current at any point in time, as well as the time constant and other important parameters of the circuit.

4. What is the time constant of an RC circuit?

The time constant of an RC circuit is a measure of how quickly the voltage across the capacitor changes in response to a change in the voltage source. It is calculated by multiplying the resistance (R) and capacitance (C) values of the circuit.

5. How do you solve differential equations for RC circuits?

Differential equations for RC circuits can be solved using various methods, such as the Laplace transform or the method of initial and final values. These methods involve manipulating the equations to solve for the voltage or current at a specific time or over a given interval.

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