RLC Circuit Problem: Finding Currents and Voltages Using Mesh Analysis

[oso0690]

Hello everybody,

So I've been on this problem for nearly 4 hours now and am still blank at what i need to do as this book only has 2 RLC circuit examples that are not helping.

 --R1-----R2--
|      |      |
Vs     L      C
|      |      |
 -------------

(well...this diagram didn't work well... basically, the Vs, L and C are parallel to each other with the L between the reistances and the Vs and C on the outsides.)
Vs = 10 + 30u(t) V, R1 = 50 Ohms, R2 = 20 Ohms, L = 10 H, C = 4 F

relevent equations: V = IR, I = C*v', L = I'


By using meshes, I am able to get the following 2 equations:

10i' + 50i = vs + 10j'

and

10j' + 20j = -vc + 10i'

where i is the current in the first mesh, j is the current in the second mesh. I'm trying to find the currents through the resistances and the voltages through the capacitance and inductance.

What do I do now? I figure I can turn the j currents into vc but that would leave i and i'.

 

[jvicens]

Hi there,

Thank you for sharing your problem with us. It sounds like you are working on a challenging RLC circuit problem. Let's see if we can help you out.

First, let's simplify the circuit by combining the parallel elements. We can do this by using the formula 1/Req = 1/R1 + 1/R2. In this case, we get Req = 50/3 Ohms. Now, we can redraw the circuit as follows:

Vs = 10 + 30u(t) V, Req = 50/3 Ohms, L = 10 H, C = 4 F

---------
| |
Vs Req
| |
---------
|
|
L
|
|
C
|
|
--------

Next, let's use Kirchhoff's voltage law to set up our equations. Since we have two unknown currents (i and j), we will need two equations. We can use the mesh current method to set up the equations as follows:

Equation 1: -10i + (50/3)i + 10j - 10 = 0 (using Kirchhoff's voltage law in the first mesh)
Equation 2: 10j + (50/3)j + (-10)j + 10i = 0 (using Kirchhoff's voltage law in the second mesh)

Now, we can solve these equations for i and j. Once we have the values for i and j, we can use them to find the currents through the resistances and the voltage through the capacitor and inductor.

I hope this helps you to move forward with your problem. Best of luck!