Engineering What Determines the Resonant Frequency in a Series RLC Circuit?

AI Thread Summary
The discussion focuses on determining the resonant frequency in a series RLC circuit with five passive components and an AC voltage source. Participants emphasize the need to find the equivalent circuit impedance using KCL equations and complex impedances for inductors and capacitors. The circuit does not allow for straightforward simplifications, as the components are neither in series nor parallel. Suggestions include analyzing the behavior of inductors and capacitors at DC and high frequencies to aid in solving the problem. Overall, the conversation highlights the complexity of the circuit and the importance of a methodical approach to find the resonant frequency.
neiks997
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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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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...
 
none of the capacitors or inductors are in parallel or series with each other?
 
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.
 
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?
 
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
 

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