Ex:           By sketching the impedance and admittance curves of series and parallel combinations of L's and C's and adding them appropriately, we can find the approximate resonance characteristics of multiple-resonant circuits. The figures show examples of these curves.

We sketch the approximate total reactance in Fig. 1 by noting that XC dominates at low frequencies and XL dominates at high frequencies.

We sketch the approximate total susceptance in Fig. 2 by noting that BL dominates at low frequencies and BC dominates at high frequencies.

 

We sketch the approximate total reactance in Fig. 3 by noting that XL dominates at low frequencies and XC dominates at high frequencies.

We sketch the approximate total reactance in Fig 4 by summing the curve from Fig. 3 and the reactance curve for C2. We find that the reactance of C2 forms a resonance with the reactance of L1C1 at a frequency below the resonance of L1C1. This new resonace is such that the entire circuit acts like a wire. There is also still a resonance at exactly the resonant frequency for L1 and C1. This resonance is such that the entire circuit acts like an open circuit, as it did before adding C2.