For a damped RLC circuit, why must R be small?

In summary, the conversation discusses the three cases for damping in mechanical or electrical systems and how the solution of the differential equation changes depending on the level of damping. It also mentions that oscillations only occur in the underdamped case due to the complex roots of the characteristic equation.
  • #1
Taulant Sholla
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5

Homework Statement


I'm reading the textbook section covering damped series RLC circuits (provided below). I'm wondering why the author stipulates "When R is small..."
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Homework Equations


Given above.

The Attempt at a Solution


Given above.
Any gentle and courteous comments are welcome!
 

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  • #2
There are three cases for damping in mechanical or electrical systems. What are they?

Hint: The solution of the differential equation describing the motion has different forms depending upon the level of damping.
 
  • #3
gneill said:
There are three cases for damping in mechanical or electrical systems. What are they?

Hint: The solution of the differential equation describing the motion has different forms depending upon the level of damping.
Ah - very helpful, thank you!
 
  • #4
Wikipedia has a very good entry (I believe so) in this subject https://en.wikipedia.org/wiki/RLC_circuit#Series_RLC_circuit

Notice the general form of the solution and how it changes in the three cases;
Underdamped, Overdamped, Critically Damped. Oscillations (to be accurate decaying oscillations) happen only in the underdamped case . That's because the characteristic equation has complex roots at this case so the exponentials of the generic solution have an oscillation term ##e^{-j\omega t}##. In the other two cases we just have exponential decay of the current.
 
Last edited:

1. What is a damped RLC circuit?

A damped RLC (resistor-inductor-capacitor) circuit is an electrical circuit that contains a resistor, an inductor, and a capacitor, arranged in a specific configuration. It is used to filter out unwanted frequencies in a signal or to control the amplitude and phase of a signal.

2. Why is RLC circuit damping important?

Damping in a circuit refers to the ability to reduce the amplitude of oscillations over time. In a damped RLC circuit, the resistor is responsible for dissipating energy, which reduces oscillations and ensures that the circuit reaches a steady-state condition. Without proper damping, the circuit can become unstable and produce unwanted behavior.

3. What is the role of R in a damped RLC circuit?

The resistor (R) in a damped RLC circuit is crucial for controlling the rate of energy dissipation and, therefore, the damping ratio. It determines the amount of resistance in the circuit and affects the overall performance of the circuit.

4. Why must R be small in a damped RLC circuit?

R must be small in a damped RLC circuit to ensure that the circuit is properly damped and stable. If R is too large, it will dissipate too much energy, leading to over-damping and a slow response. On the other hand, if R is too small, the circuit will be under-damped, leading to oscillations and potential instability.

5. Can R be completely eliminated in a damped RLC circuit?

No, R cannot be completely eliminated in a damped RLC circuit. As mentioned earlier, R is responsible for dissipating energy, and without it, the circuit would become unstable. However, the value of R can be minimized to achieve the desired damping ratio for a particular circuit application.

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