Homework Help: Resonant circuit

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.

 

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.