How to calculate the resonance frequency of a parallel LC circuit with L having a DC resistance?
How can I calculate the resonance frequency?


It's quite straightforward if you'll take the time to think about it.

By definition, the resonance frequency is, in this context, the frequency at which the impedance of the equivalent impedance is real.

The branch with the R and L has an impedance of:  \$R + j\omega L\$

The branch with the C has an impedance of:  \$\dfrac{1}{j \omega C} \$

Now, the equivalent impedance is just:

\$(R + j\omega L)||\dfrac{1}{j \omega C}\$

The resonance frequency is the frequency for which the above is purely real, i.e., set the imaginary part of the above equal to zero and solve for the frequency.

When you do this correctly, you should get



or equivalently, as the Wikipedia link Renan gives:

\$\omega_0 = \sqrt {\frac{1}{LC} - \left ( \frac{R}{L} \right )^2}\$