Calculate Values of L and C

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In summary, the given problem involves an RLC circuit with a resonance frequency of 2000/π hertz. The reactance of inductance is 12 ohms and the reactance of capacitance is 8 ohms when operating at an angular frequency higher than the resonance frequency. To find the values of L and C, the equations XL = wL and XC = 1/wC can be used, along with a third equation derived from XL-XC=0. This equation can be solved to find the frequency that makes XL 12 ohms and XC 8 ohms, which can then be used to calculate L and C.
  • #1
wayneinsane
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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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  • #2
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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  • #3
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..
 
  • #4
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. [tex] \omega=2 \pi f[/tex]. When RLC circuit resonates, XL-XC=0. You can derive the third equation from that.
 
  • #5
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!
 
  • #6
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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1. How do I calculate the value of L in an LC circuit?

To calculate the value of L in an LC circuit, you will need to know the frequency of the circuit and the capacitance (C) value. You can then use the formula L = 1/(4π²f²C), where f is the frequency in hertz. This will give you the value of L in henries (H).

2. What is the role of L and C in an LC circuit?

L and C, or inductance and capacitance, are two essential components in an LC circuit. L represents the inductance, which is the ability of the circuit to store energy in a magnetic field. C represents the capacitance, which is the ability of the circuit to store energy in an electric field. Together, they create a resonant circuit that can store and release energy at a specific frequency.

3. How does the value of L affect the resonant frequency of an LC circuit?

The value of L directly affects the resonant frequency of an LC circuit. As the value of L increases, the resonant frequency decreases. This is because a larger inductance value requires a lower capacitance value to maintain the same resonant frequency. Conversely, a smaller inductance value will result in a higher resonant frequency.

4. Can I calculate the value of C if I know the value of L and the resonant frequency?

Yes, you can calculate the value of C if you know the value of L and the resonant frequency. You can use the formula C = 1/(4π²f²L), where f is the resonant frequency in hertz and L is the inductance value in henries. This will give you the capacitance value in farads (F).

5. How do I use the values of L and C to calculate the impedance of an LC circuit?

To calculate the impedance of an LC circuit, you will need to use the formula Z = √(R² + (ωL - 1/ωC)²), where R is the resistance of the circuit, ω is the angular frequency (2πf), L is the inductance value, and C is the capacitance value. This formula takes into account all the components in the circuit and will give you the total impedance in ohms (Ω).

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