Is My Critically Damped RLC Circuit Formula Correct?

In summary, a critically damped RLC circuit is an electrical circuit containing a resistor, inductor, and capacitor in series. It is in a state of critical damping when the damping factor is equal to the square root of the product of the inductance and capacitance. This causes the circuit to return to equilibrium without any oscillation or overshoot. It differs from overdamped and underdamped circuits as the damping factor is greater or less than the square root of the product of the inductance and capacitance, respectively. Some applications of a critically damped RLC circuit include audio amplifiers, power supplies, and control systems. The damping factor can be calculated by dividing the resistance by two times the square root of the product
  • #1
gfd43tg
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Hello, I am working on this problem

ImageUploadedByPhysics Forums1399262763.143729.jpg


However, I am getting a 900t term that the solution is lacking. I am wondering if what I did was wrong. My formula is consistent with the formula for a series RLC circuit that is critically damped.

ImageUploadedByPhysics Forums1399262780.749543.jpg
 
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Check: What is the sign of dVC/dt at time t = 0+ ? Hint: In which direction is the initial current flowing?
 
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oh, I see. Thanks!
 

FAQ: Is My Critically Damped RLC Circuit Formula Correct?

1. What is a critically damped RLC circuit?

A critically damped RLC circuit is an electrical circuit that contains a resistor (R), inductor (L), and capacitor (C) in series. It is considered to be in a critically damped state when the damping factor is equal to the square root of the product of the inductance and capacitance, also known as the natural frequency. This means that the circuit will return to its equilibrium state without any oscillation or overshoot.

2. How is a critically damped RLC circuit different from an overdamped or underdamped circuit?

In an overdamped RLC circuit, the damping factor is greater than the square root of the product of the inductance and capacitance, resulting in a slower return to equilibrium and no oscillation. In contrast, an underdamped RLC circuit has a damping factor less than the square root of the product of the inductance and capacitance, causing it to oscillate before settling to its equilibrium state.

3. What are the applications of a critically damped RLC circuit?

A critically damped RLC circuit is commonly used in electronic devices such as audio amplifiers, power supplies, and filters. It is also used in control systems to prevent overshooting or oscillation in response to a sudden change in input.

4. How do you calculate the damping factor of a critically damped RLC circuit?

The damping factor (ζ) of a critically damped RLC circuit can be calculated by dividing the resistance (R) by two times the square root of the product of the inductance (L) and capacitance (C). ζ = R / 2√(L*C)

5. How can you tell if an RLC circuit is critically damped?

To determine if an RLC circuit is critically damped, you can calculate the damping factor and compare it to the square root of the product of the inductance and capacitance. If they are equal, the circuit is critically damped. You can also observe the response of the circuit to a sudden change in input. If it returns to equilibrium without any oscillation or overshoot, it is likely in a critically damped state.

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