What Determines the Resonant Frequency in a Series RLC Circuit?

In summary, the student is trying to find an equivalent circuit for a set of passive components that produce a sinusoidal voltage at a fixed frequency. They are clueless on how to do this and are looking for help from the community. Parts 2 and 3 of the problem should be completed first to see if the circuit becomes more simplified. If not, they can try to solve for Z using the KCL equations.
  • #1
neiks997
3
0

Homework Statement


I will give a circuit of 5 passive components and an AC voltage source producing a sinusoidal voltage at a fixed frequency of omega / (2*pi) Hz.
i will post a picture asking what is being looked for along with the circuit.

Homework Equations


z = R + jwL + 1 / jwc, jw0L + 1 / jw0c = 0, w0 = 1/ sqrt(LC), B = w2 - w1 = R/L = w0/Q, Q = w0L / R = 1/w0RC, w1 = w0 - B/2, w2 = w0 + B/2


The Attempt at a Solution


clueless on how to make an equivalent circuit.
 

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  • #2
neiks997 said:

Homework Statement


I will give a circuit of 5 passive components and an AC voltage source producing a sinusoidal voltage at a fixed frequency of omega / (2*pi) Hz.
i will post a picture asking what is being looked for along with the circuit.

Homework Equations


z = R + jwL + 1 / jwc, jw0L + 1 / jw0c = 0, w0 = 1/ sqrt(LC), B = w2 - w1 = R/L = w0/Q, Q = w0L / R = 1/w0RC, w1 = w0 - B/2, w2 = w0 + B/2


The Attempt at a Solution


clueless on how to make an equivalent circuit.

Welcome to the PF.

It says it wants you to find the equivalent circuit impedance Z that is formed by those components in that configuration.

There are no obvious simplifications of the circuit, so you need to write the KCL equations for the circuit, to find the Z = Vin/Iin impedance. Use the complex impedances for the L and C components...
 
  • #3
none of the capacitors or inductors are in parallel or series with each other?
 
  • #4
neiks997 said:
none of the capacitors or inductors are in parallel or series with each other?

Nope. That's why you need to write the KCL equations to solve this.
 
  • #5
I'd be tempted to do parts 2 and 3 first. What happens to L's and C's at DC and very high frequencies?

It's been many years since I did this but I half remember a trick that relies on the impedance of the source being low to simplify the circuit?
 
  • #6
CWatters said:
I'd be tempted to do parts 2 and 3 first. What happens to L's and C's at DC and very high frequencies?

It's been many years since I did this but I half remember a trick that relies on the impedance of the source being low to simplify the circuit?

brilliant
 

FAQ: What Determines the Resonant Frequency in a Series RLC Circuit?

What is a series resonance circuit?

A series resonance circuit is an electrical circuit that consists of a resistor, inductor, and capacitor connected in series. It is also known as an RLC circuit and is used to study the behavior of an electric current under resonance conditions.

How does a series resonance circuit work?

In a series resonance circuit, the inductor and capacitor store energy back and forth between them, causing the current to oscillate at the resonant frequency. This results in a higher amplitude of current and a lower impedance, making it easier for the current to flow through the circuit.

What is the resonant frequency in a series resonance circuit?

The resonant frequency in a series resonance circuit is the frequency at which the inductive reactance and capacitive reactance are equal. This results in the lowest impedance and the highest amplitude of current in the circuit.

What is the importance of a series resonance circuit?

Series resonance circuits have many practical applications, such as in radio and television receivers, electronic filters, and power factor correction circuits. They also help in understanding the behavior of electrical circuits under resonance conditions, which is important in many engineering and scientific fields.

How can I calculate the resonant frequency of a series resonance circuit?

The resonant frequency of a series resonance circuit can be calculated using the formula 1/2π√(LC), where L is the inductance of the circuit and C is the capacitance. Alternatively, it can also be calculated using the formula ω=1/√(LC), where ω is the angular frequency.

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