Solve Resonant Circuit Problem with 220mH & 6 Ohms

[christian_419]

hello,
im a quite stuck on how to answer this question on resonant circuits. any help would be most appreciated!

Homework Statement

a coil of inductance 220mH and resistance 6 ohms is connected in parrallel with a capacitor across a 230volt variable supply. if the circuit goes into resonance at a frequency of 9.9KHz determine:
i) the capacitance of the circuit taking into account the resistance?

The Attempt at a Solution

i have tried working out XL with using the 2pi*f*L formula but wasnt sure if the resonace frequency was the correct frequency to use and also how would i then transpose the above ciruit information to give me C?

thank you very much for any help offered.

 

[berkeman]

hello,
im a quite stuck on how to answer this question on resonant circuits. any help would be most appreciated!

Homework Statement

a coil of inductance 220mH and resistance 6 ohms is connected in parrallel with a capacitor across a 230volt variable supply. if the circuit goes into resonance at a frequency of 9.9KHz determine:
i) the capacitance of the circuit taking into account the resistance?

The Attempt at a Solution

i have tried working out XL with using the 2pi*f*L formula but wasnt sure if the resonace frequency was the correct frequency to use and also how would i then transpose the above ciruit information to give me C?

thank you very much for any help offered.

Welcome to the PF. What does this mean?

"i) the capacitance of the circuit taking into account the resistance?"

Do they want the reactance? There is no "capacitance" per se, other than the cap that is in the circuit. Also, are the R and L in series or in parallel. It's not clear from the problem as stated.

 

[christian_419]

hi, i don't know if the resitor or inductor are in series or parallel, that was all the question stated.
I think its looking for me to look at the relation between XL and XC at resonance and then work out XL to give me XC and transpose the XC formula to get "C".
Does that sound like it would answer the question?
I know this doesn't take into account the resistor though, is this to just be ignored?

 

[berkeman]

hi, i don't know if the resitor or inductor are in series or parallel, that was all the question stated.
I think its looking for me to look at the relation between XL and XC at resonance and then work out XL to give me XC and transpose the XC formula to get "C".
Does that sound like it would answer the question?
I know this doesn't take into account the resistor though, is this to just be ignored?

The original question sounded like the resistor was supposed to be part of the solution. But I'm also confused, because at resonance, XL and XC should cancel, no? Sorry I'm not of much help[ on this question -- pretty confusing.

 

[christian_419]

thanx for your help anyway, its much appreciated

 

[vela]

The inductor is not ideal, so you need to model it as an ideal inductor L in series with a resistor R. This combination is placed in parallel to the capacitor C and the voltage source. I think the resistance screws up just comparing the reactances directly (though I could very well be wrong). It should be straightforward, though tedious, to find the response of this circuit to a sinusoidal input and derive an expression for the resonance frequency in terms of R, L, and C.

 

[The Electrician]

Generally, capacitors can be nearly ideal, but inductors tend to be quite a bit less than ideal.

The OP's problem statement said "...a coil of inductance 220mH and resistance 6 ohms...".

To me that sounds like the inductor winding has a resistance of 6 ohms.

Then the circuit is a inductance of 220mH in series with 6 ohms; that series combination is then in parallel with a capacitor, C.

The solution to the problem can be had by calculating the equivalent impedance of all that, and equating the imaginary part to zero (that's resonance).

 

[Adjuster]

Generally, capacitors can be nearly ideal, but inductors tend to be quite a bit less than ideal.

The OP's problem statement said "...a coil of inductance 220mH and resistance 6 ohms...".

To me that sounds like the inductor winding has a resistance of 6 ohms.

Then the circuit is a inductance of 220mH in series with 6 ohms; that series combination is then in parallel with a capacitor, C.

The solution to the problem can be had by calculating the equivalent impedance of all that, and equating the imaginary part to zero (that's resonance).

There is an interesting point to take from this example: in radio work it is usual to have tuning inductances made as low-loss (high Q) as possible. Thus normally the effective series resistance will only be a very small percentage of the reactance. The approximation that we have resonance when XC=XL will be only slightly in error.

In power contexts the components are often much lossier (lower Q), and ignoring the loss resistances would lead to more appreciable errors.