Understanding RLC Circuits: Critical Damping & Homework Equations

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In summary, the conversation involves discussing the use of critical damping in RLC circuits and asking for clarification on how to solve for different constants and which components to consider in calculations. The conversation also includes an incorrect calculation and diagram that are addressed.
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dwn
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Homework Statement



Image

Homework Equations



Critical Damping

* related to '*' on image : diL/dt = -vc(0) - Ri(0)
When do we use this to solve for the other constant? In the text, an example problem is never fully explained in mathematical terms.

The Attempt at a Solution



I am looking for someone to kind of explain what to keep an eye out for when analyzing RLC circuits, or provide a source. I have looked through a couple different textbooks and certain things vary and its leading to confusion. One particular concern is after we calculate whether a circuit is over/under damped or critical (I know the characteristic equations for each), are we solving vc or iL. Now I'm sure it depends on what the question asks, but sometimes it includes both instances. Can someone please sort this out for me?**EDIT**
The voltage for capacitor should be 12/5 = 2.4 Correct?
 

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  • #2
dwn said:


**EDIT**
The voltage for capacitor should be 12/5 = 2.4 Correct?


Incorrect. What is the total resistance in series with L?

Also, your t(0+) diagram is wrong. The 1 ohm resistor has mysteriously migrated away from C!
 

1. What is an RLC circuit?

An RLC circuit is an electrical circuit that contains a resistor (R), inductor (L), and capacitor (C) components. These components are connected in series or parallel and can be used to control the flow of current and voltage in the circuit.

2. What is critical damping in an RLC circuit?

Critical damping in an RLC circuit occurs when the damping factor is equal to the natural frequency of the circuit. This means that the circuit will return to its equilibrium state without any oscillation, resulting in a smooth and stable response.

3. How is critical damping calculated in an RLC circuit?

The damping factor (ζ) in an RLC circuit can be calculated by dividing the resistance (R) by two times the square root of the inductance (L) multiplied by the capacitance (C). If the damping factor is equal to the natural frequency of the circuit, it is considered to be critically damped.

4. What are the homework equations for solving RLC circuits?

The homework equations for solving RLC circuits depend on the type of circuit and the desired outcome. Some commonly used equations include Ohm's Law (V=IR), Kirchhoff's Voltage Law (ΣV=0), and the formula for calculating the impedance (Z) of a series RLC circuit (Z=√(R^2+(XL-XC)^2)).

5. How can understanding RLC circuits be useful?

Understanding RLC circuits can be useful for designing and analyzing electronic circuits, as well as troubleshooting problems in electrical systems. It is also important for engineers and scientists working in fields such as telecommunications, power systems, and signal processing.

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