Equivalent Resistance of an RLC circuit

[wiz0r]

Homework Statement

It is in the attachment.

NOTE: I supposed I did a little mistake when I drew the circuit with PSpice. The closed switch should look like .---->. instead of having that 45 angle. I don't know if it matters or not, so yea..

Homework Equations

Rp = (R1 * R2)/ (R1 + R2)
Rs = R1 + R2 + R3 + ... + Rn
α(series) = Req / (2*L)
Wo = 1/sqrt(LC)

The Attempt at a Solution

Okay, well, I'm trying to solve this second order transient circuit, but I have a problem! I can't find the correct equivalent resistance. What I do first is to remove the voltage source by a short and the current source by an open circuit. Now, I got to find the equivalent resistance to calculate α. What I do is;

R12 = (2 * 6) / (2 + 6) = 1.5 ohms

then;

Req = R12 + R3 + R4 = 1.5 + 4 + 2 = 7.5 ohms

According to the book, the Req should be 2 ohms! So either, I'm doing something really wrong, or there's a mistake with the book. Can someone please help me?

Any help would be greatly appreciated.

 

[wiz0r]

mm, well, i figured out what was wrong.

since the switch is closed, i need it to open it to find the equivalents R, L, and C to check if its an series RLC or parallel RLC.

i opened the switch, and took out the sources, everything cancels out, and i'll have only the rightmost loop with the 2 ohm resistance, 2H inductance, and 1F capacitance.

anyway, could somone tell me if I am right or not?

 

[Moetasim]

Thank you for reaching out with your question. It's great to see that you are trying to solve this circuit on your own and seeking help when you encounter difficulties. I can provide some guidance on how to approach this problem.

First, let's review the concept of equivalent resistance. In a series circuit, the equivalent resistance is simply the sum of all the individual resistances. In a parallel circuit, the equivalent resistance is calculated using the formula Rp = (R1 * R2) / (R1 + R2). In this circuit, we have both series and parallel components, so we need to use both formulas to find the total equivalent resistance.

To start, let's simplify the circuit by removing the voltage source and current source as you have done. This leaves us with a series circuit composed of R1, R2, R3, and R4. The equivalent resistance for this series circuit is simply the sum of all the resistances, which is 6 + 2 + 4 + 2 = 14 ohms.

Now, let's consider the parallel components. R1 and R2 are in parallel, so we can use the formula Rp = (R1 * R2) / (R1 + R2) to find their equivalent resistance. This gives us Rp = (6 * 2) / (6 + 2) = 1.5 ohms.

Next, we need to add this equivalent resistance to the series circuit we calculated earlier. This gives us Req = 1.5 + 4 + 2 = 7.5 ohms.

So, the equivalent resistance for this circuit is 7.5 ohms, which matches your calculation. I'm not sure where the 2 ohms in the book came from, but it may be a typo or a different approach to solving the problem.

I hope this helps clarify the concept of equivalent resistance and how to calculate it in a circuit with both series and parallel components. Keep up the good work in your studies and don't hesitate to reach out for help when needed. Good luck!