What are the Unknowns in a RLC Circuit with Resonance Frequency and Impedance?

In summary, the resonant frequency of a RLC circuit is 6 KHz, and when driven by a 8 KHz ac generator, it has an impedance of 1 k W.
  • #1
zakaqel
10
0

Homework Statement



A RLC circuit has a resonance frequency of 6 KHz. When it is driven by a 8 KHz ac generator, it has an impedance of 1 k W. What are R, L and C in the circuit?



Homework Equations





The Attempt at a Solution



the equation for the resonant frequency will be
fo = 1 / 2 π √(L C)
the equation for the impedence will be
Z = √[R2 + (XL - XC)^2]
where XL = 2 π f L

XC = 1 / 2 π f C
f = 8 x 10^3 Hz
fo = 6 x 10^3 Hz
Z = 1 x 10^3 Ω

How am I supposed to solve for the three unkowns(R,L,C) with only two equations? Is there a third relationship for R?
 
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  • #2
Are you sure there is no impedence at resonance given?
 
  • #3
No impedance at resonance is given. That's what I was thinking...it'll be impossible to solve if you don't have a relation for R.
 
  • #4
Is your circuit series or parallel?
And what is this: "...it has an impedance of 1 k W"? Do you mean kohm of the circuit or the generator?
 
  • #6
dlgoff said:
Is your circuit series or parallel?
And what is this: "...it has an impedance of 1 k W"? Do you mean kohm of the circuit or the generator?

I think he used the Latinized W instead of Ω.
 
  • #7
well, the question was given by my professor. I am 100% sure that there is a piece of informaiton missing from the original question.

BTW, the RLC is connected in series.
 
  • #8
It turns out that he forgot to say that the phase angle=45 degrees...ugghhhh...It's an easy one now.

Thanks for the help!
 
  • #9
zakaqel said:
It turns out that he forgot to say that the phase angle=45 degrees...ugghhhh...It's an easy one now.

Thanks for the help!

Alrighty then. There's your third equation.

Good luck.
 

FAQ: What are the Unknowns in a RLC Circuit with Resonance Frequency and Impedance?

1. What is an RLC circuit?

An RLC circuit is an electrical circuit that contains a resistor (R), an inductor (L), and a capacitor (C). These components are connected in series or in parallel and can be used to filter or manipulate the frequency of an electrical signal.

2. What is the resonant frequency of an RLC circuit?

The resonant frequency of an RLC circuit is the frequency at which the inductive and capacitive reactances cancel each other out, resulting in a purely resistive circuit. This frequency can be calculated using the formula f0 = 1 / (2π√(LC)), where f0 is the resonant frequency, L is the inductance, and C is the capacitance.

3. How does the frequency affect an RLC circuit?

The frequency of an RLC circuit can affect its behavior in several ways. At the resonant frequency, the circuit will have a high impedance, making it difficult for current to flow through. At frequencies below the resonant frequency, the circuit will have a low impedance and will act like a wire, allowing current to flow easily. At frequencies above the resonant frequency, the circuit will have a high impedance again, but with a phase shift that can be used to filter specific frequencies.

4. How can the frequency response of an RLC circuit be graphed?

The frequency response of an RLC circuit can be graphed using a Bode plot, which shows the gain and phase shift of the circuit at different frequencies. The x-axis represents the logarithm of the frequency, and the y-axis represents the gain in decibels or the phase shift in degrees.

5. How can the frequency of an RLC circuit be adjusted?

The frequency of an RLC circuit can be adjusted by changing the values of the inductor, capacitor, or resistor. Increasing the inductance or capacitance will lower the resonant frequency, while increasing the resistance will raise it. Additionally, the frequency can be adjusted by changing the input voltage or by adding external components, such as a transformer or filter, to the circuit.

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