How Do You Calculate L and C in an RLC Circuit with Given Reactances?

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To calculate the values of inductance (L) and capacitance (C) in an RLC circuit with a resonance frequency of 2000/pi hertz, it's essential to understand that the given reactances of 12 ohms for inductance and 8 ohms for capacitance are at an angular frequency greater than the resonance frequency. The angular frequency, denoted as w, is not the same as the resonance frequency, which is often represented as w0. The equations XL = wL and XC = 1/wC must be used correctly, taking into account that the resonance condition (XL - XC = 0) needs to be derived to find the appropriate frequency for the given reactances. The calculations should isolate w to determine the frequency that results in the specified reactance values. Accurate application of these principles will yield the correct values for L and C.
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Homework Statement




An RLC circuit has a resonance frequency of 2000/pi hertz. When operating at angular frequency w > w0, reactance of inductance is 12 ohms and reactance of capacitance is 8 ohms. Calculate the values of L and C.

Homework Equations



XL = wL
XC = 1/wC


The Attempt at a Solution


welll, what i thouht was w = resonance frequency which is 2000/pi hertz... so since XL is given (12) and XC is given (8), then I plugged in the numbers and got this.

2000/pi = 636.6 hz...so, XL/w = L
12/636.6hz = .0188 H = L

and, 1/wXC = C which is 1/(636.6)(8) = .000196F = C

Correct or not? I feel like something is missing!
 
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Your answer isn't correct. There are a couple of things you're doing wrong. First of all, frequency isn't the same as angular frequency. And second, you're calculating the reactances of L and C using the resonance frequency, when values are given with higher frequency in the problem. You'll need three equations to solve this one, you've got two of them. Do you have an equation for resonance frequency or can you perhaps derive it with the knowledge you've got?
 
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But isn't w the symbol for resonance frequency? and resonance frequency is given in the problem, along with the reactance of capaciatance and inductance...im not sure what other equation I would need..
 
wayneinsane said:
But isn't w the symbol for resonance frequency? and resonance frequency is given in the problem, along with the reactance of capaciatance and inductance...im not sure what other equation I would need..

Nope. The w is the angular frequency (i.e. how fast sinusoidal signal goes through one cycle), the angular frequency for the resonance frequency is usually denoted by w0. There is link between angular frequency and frequency, though. \omega=2 \pi f. When RLC circuit resonates, XL-XC=0. You can derive the third equation from that.
 
Hmm, this is starting to make sense... I just checked my notes and you are absolutely right. Wo is the resonance frequency...

so... since w = 2 pi f, and XL = wL... can I do XL = 2 pi f L which would be XL/2 pi f = L, so 12/4000 which is 3 x 10-3...

then, for XC = 1/wC, can I do XC = 1/2pi f C, which would rearrange to C = 1/XC 2 pi f which would be 1/8x4000 which is 3.125x10-5...

correct?

BTW, thank's a lot!
 
Still not correct. Seems like my earlier point didn't go across the way I meant. This sentence "When operating at angular frequency w > w0, reactance of inductance is 12 ohms and reactance of capacitance is 8 ohms." says, that XL is 12 ohms and XC is 8 ohms at some unknown frequency, that is higher than the resonance frequency. So you can't use the resonance frequency to directly determine L and C, like you are now trying to. Solve XL-XC=0 as a function of L and C (i.e. isolate the w to one side and the rest to the other) to get the third equation. From there you can solve the frequency that makes XL 12 ohms and XC 8 ohms.
 
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Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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