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

[zakaqel]

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?

 

[LowlyPion]

Are you sure there is no impedence at resonance given?

 

[zakaqel]

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.

 

[dlgoff]

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?

 

[LowlyPion]

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.

I recall a very similar problem but the Impedance at resonance was given:
https://www.physicsforums.com/showthread.php?t=251778&highlight=impedence

 

[LowlyPion]

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.

 

[zakaqel]

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.

 

[zakaqel]

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!

 

[LowlyPion]

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.