Resonant frequency of a circuit

In summary, the resonant frequency of a circuit is the frequency at which the circuit naturally oscillates with the greatest amplitude, and it can be calculated using the formula f<sub>r</sub> = 1 / (2&pi;&radic;(LC)). The values of inductance and capacitance in the circuit, as well as the type of circuit and presence of external resistance, affect the resonant frequency. Resonant frequency is important in circuit design for efficient energy transfer and component selection, and it can be adjusted by changing the values of inductance or capacitance.
  • #1
gfd43tg
Gold Member
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Hello, I am working on this circuit to find the resonant frequency.
ImageUploadedByPhysics Forums1398753368.063181.jpg


I calculate 10^8 rad/s, but the solution says it's 10^4 rad/s. Here is my work. I just solved for the equivalent impedance, and then separated the j term and solved for the inside of the parenthesis to be equal to zero.

ImageUploadedByPhysics Forums1398753450.226063.jpg


Am I wrong or the solution?
Thank you
 
Last edited:
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  • #2
Hey, you should make imaginary part of impedance zero not the whole equation because at resonance the circuit will be purely resistive ...impedance doesnot equal zero
 
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  • #3
Thank you very much, I solved it now!
 

Related to Resonant frequency of a circuit

What is the resonant frequency of a circuit?

The resonant frequency of a circuit is the frequency at which the circuit will naturally oscillate, or vibrate, with the greatest amplitude. This means that the circuit will have the highest amount of energy at this frequency.

How is the resonant frequency of a circuit calculated?

The resonant frequency of a circuit can be calculated using the formula fr = 1 / (2π√(LC)), where fr is the resonant frequency, L is the inductance of the circuit, and C is the capacitance of the circuit. This formula is valid for series resonance in an LC circuit.

What factors affect the resonant frequency of a circuit?

The resonant frequency of a circuit is affected by the values of inductance (L) and capacitance (C) in the circuit. Additionally, the type of circuit (series or parallel) and the presence of any external resistance can also affect the resonant frequency.

Why is resonant frequency important in circuit design?

Resonant frequency is important in circuit design because it allows for the efficient transfer of energy between different components in the circuit. It also helps in the selection and tuning of components to achieve the desired frequency response.

How can the resonant frequency of a circuit be adjusted?

The resonant frequency of a circuit can be adjusted by changing the values of inductance (L) or capacitance (C) in the circuit. This can be done by using different components or by adjusting the physical properties of the existing components, such as the length of a coil or the distance between capacitor plates.

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