How Do You Calculate Impedance in a Resonant RLC Circuit?

[maobadi]

Homework Statement

Quick one guys, I am very confused about the impedance of a RLC circuit. Say when you have more than one resistor or more than one capacitor or inductor in different combination, you get a impedance with two parts(imaginary which is the reactive part and the resistive part) when the circuit is in resonance, how do I find the actual impedance because all the reactive parts cancels out.

Homework Equations

and what is the behaviour of resistor above resonance frequency...?

The Attempt at a Solution

I am stuck...

 

[berkeman]

Homework Statement

Quick one guys, I am very confused about the impedance of a RLC circuit. Say when you have more than one resistor or more than one capacitor or inductor in different combination, you get a impedance with two parts(imaginary which is the reactive part and the resistive part) when the circuit is in resonance, how do I find the actual impedance because all the reactive parts cancels out.

Homework Equations

and what is the behaviour of resistor above resonance frequency...?

The Attempt at a Solution

I am stuck...

Write the equation for a parallel RLC circuit, and solve for the Z(resonance). What do you get?

Do the same for a series RLC circuit -- what do you get for Z(resonance)?

 

[Mene]

it is important to have a clear understanding of the concepts and equations involved in a problem before attempting to solve it. In this case, the impedance of a RLC circuit can be calculated using the formula Z = √(R^2 + (XL - XC)^2), where R is the resistance, XL is the inductive reactance, and XC is the capacitive reactance.

To find the actual impedance at resonance, you can set XL = XC, which will result in an impedance of Z = R. This means that at resonance, the reactive parts will indeed cancel out, leaving only the resistive part.

As for the behavior of a resistor above resonance frequency, it will act as a normal resistor, with its resistance value determining the overall impedance of the circuit. It is important to note that above resonance frequency, the inductor and capacitor will have less impact on the overall impedance, as their reactances decrease with increasing frequency.

In summary, to find the actual impedance at resonance, set XL = XC and solve for Z using the formula provided. And above resonance frequency, the behavior of a resistor will be determined by its resistance value. I hope this helps clarify your confusion.

 

[Mene]

it is important to understand the concept of impedance in a RLC circuit. Impedance is a measure of the opposition to the flow of current in a circuit. In a resonant circuit, the impedance is at its minimum value, resulting in a maximum flow of current.

To find the actual impedance of a RLC circuit, you can use the equation Z = √(R² + (Xl - Xc)²), where R is the resistance, Xl is the inductive reactance, and Xc is the capacitive reactance. This equation takes into account the real and imaginary components of the impedance, giving a single value for the overall impedance.

As for the behavior of a resistor above the resonance frequency, it will have a higher impedance compared to when it is at the resonance frequency. This is because at resonance, the inductive and capacitive reactances cancel each other out, resulting in a lower overall impedance. Above resonance, the inductive and capacitive reactances will not cancel each other out, leading to a higher overall impedance.

I hope this helps clarify the concept of impedance in a RLC circuit. Keep practicing and seeking help when needed, as understanding this concept is crucial in the field of science.