Difference equation of simple RLC Circuit

[Eng67]

I have been having a difficult time understanding how to determine the input/output difference equations of a circuit. I believe I am good on series circuits but would like some feedback on Series/parallel determinations. Please look at included file and see if I am on the correct path.

 

[doodle]

Are you sure the answer you gave is correct?

I got
L d2(i_R)/dt2 + R d(i_R)/dt + (1/C) i_R = L d2(i)/dt2 + (1/C) i

or if you can render in Latex
$$L \frac{d^2 i_R}{dt^2} + R \frac{di_R}{dt} + \frac{i_R}{C} = L \frac{d^2 i}{dt^2} + \frac{i}{C}$$

 

[piercas]

The difference equation of a simple RLC circuit can be determined by analyzing the circuit using Kirchhoff's laws and applying the concept of voltage and current division. The input/output difference equation can be obtained by solving for the voltage or current at either the input or output node, depending on the desired output.

In a series RLC circuit, the input/output difference equation can be written as:

Vout = Vin * (Zout / (Zout + Zin))

where Vin is the input voltage, Vout is the output voltage, Zin is the total impedance of the input components (resistor, inductor, and capacitor), and Zout is the total impedance of the output components. This equation shows that the output voltage is a function of the input voltage and the impedance values of the circuit components.

In a parallel RLC circuit, the input/output difference equation can be written as:

Iout = Iin * (Zin / (Zin + Zout))

where Iin is the input current, Iout is the output current, Zin is the total impedance of the input components, and Zout is the total impedance of the output components. This equation shows that the output current is a function of the input current and the impedance values of the circuit components.

To determine the input/output difference equations of a series/parallel RLC circuit, you can use the same approach of applying Kirchhoff's laws and voltage/current division. It is important to note that the impedance values of the components in a series/parallel circuit will differ from those in a simple series or parallel circuit, so you may need to use different equations to calculate them.

I recommend further studying the concepts of series/parallel circuits and practicing with different examples to improve your understanding and accuracy in determining the input/output difference equations. Additionally, seeking feedback and guidance from a teacher or mentor can also be helpful in clarifying any doubts or misconceptions.