I am trying to see if I understand how impedance works correctly before I build this into a real circuit. Basically I have an inductor (helmholtz coil) driven by a function generator, now by itself we know the higher the freq goes the lower the current the coil will receive. If my understanding is correct, I can put a capacitor in parallel with the coil, which would mean at higher frequencies the Xc would decrease and Xl would increase, but since they are in parallel Xtot should decrease, thus as a result you will get a higher current at the same frequency than if we had just had a inductor (coil) in the circuit by itself. Is this understanding correct? Or is there a smarter way to increase the current my circuit receives at a higher frequency, besides increasing the current outputed by the generator/changing the coil design itself.
p.s. this is a re-expression of the question asked here Impedance for Helmholtz Coil Connected to Audio Amplifier but in a more detailed and precise way I hope
Best Answer
That's not automatically true for complex impedances. For the inductor \$Z_L = j\omega L\$, for the capacitor \$Z_C = \dfrac{1}{j \omega C}\$. Both in parallel gives
\$ Z = \dfrac{j\omega L \cdot \dfrac{1}{j \omega C}}{j\omega L + \dfrac{1}{j \omega C}} = \dfrac{j\omega L \cdot \dfrac{1}{j \omega C}}{\dfrac{j^2 \omega^2 LC + 1}{j \omega C}} = \dfrac{j\omega L}{1 - \omega^2 LC} \$
The minus sign in the denominator is interesting. Since \$\omega^2 LC\$ is positive, we can find a value for it where the denominator becomes zero.
\$ \omega^2 LC = 1\$
or
\$ \omega = \sqrt{\dfrac{1}{LC}} \$
If the denominator is zero the impedance is infinite. That goes against intuition which says that paralleling two components will give a lower impedance than the lowest of the two.
The image gives the explanation. Currents through \$C\$ and \$L\$ are at 90° with voltage, but in opposite directions. If their magnitudes are different their sum will be either a capacitive or inductive current. But when they're equal the sum is zero. No current. A zero current for a non-zero voltage means infinite impedance.
The frequency for which this is true is the resonance frequency, and it's used to make oscillators and high-Q filters.