RLC circuit with more the 2 storage elements

[elimenohpee]

Homework Statement

There is no real problem, so I'll just make up a arbitrary one. A series RLC circuit with a voltage source x(t), but say there is a resistor in parallel with the capacitor, followed by an inductor in parallel with that resistor. Just assume all the values of the inductors, resistors, and capacitor are 1 to make it easy.

Homework Equations

How would you derive a differential equation for an RLC circuit that contains more than 2 storage elements? I know the equation should be a 3rd order DE since it'll contain 3 storage elements, but I don't really know how to go about finding it. I can do series and parallel RLC's fine, but when it involves an extra storage element i get thrown off.

 

[Valkarie]

Any help would be appreciated.The answer is:The differential equation for an RLC circuit involving two or more storage elements is given by: L₁ * d²x(t)/dt² + (R + R₁) * dx(t)/dt + 1/C₁ * x(t) + 1/C₂ * ∫x(t)dt = x(t) Where L₁ is the inductance of the first inductor, R is the resistance of the resistor, R₁ is the resistance of the parallel resistor, C₁ is the capacitance of the capacitor, and C₂ is the capacitance of the parallel capacitor.

 

[Mene]

I can provide you with a general approach to deriving a differential equation for an RLC circuit with more than 2 storage elements. First, we need to understand the behavior of each individual element in the circuit. The resistor, capacitor, and inductor each have their own equations that describe their response to changes in voltage and current.

Next, we need to consider the overall behavior of the circuit. This can be done by applying Kirchhoff's laws and using the concept of conservation of energy. We can also use the concept of impedance to analyze the circuit.

Once we have a good understanding of the individual elements and the overall circuit behavior, we can combine these insights to derive a differential equation for the circuit. This equation will take into account the interactions between the different elements and their effects on the overall response of the circuit.

In the case of an RLC circuit with more than 2 storage elements, we would need to consider the interactions between all three elements and their effects on the voltage and current in the circuit. This would result in a third-order differential equation, as you correctly mentioned.

To solve this differential equation, we can use various mathematical techniques such as Laplace transforms or numerical methods. The specific method chosen would depend on the nature of the problem and the desired level of accuracy.

In summary, deriving a differential equation for an RLC circuit with more than 2 storage elements involves understanding the behavior of each individual element, analyzing the overall circuit behavior, and combining these insights to create a comprehensive equation. I hope this helps you in your homework assignment.