A small intro:
We have mainly three types of electronic-devices with their characteristic property:
- Resistor with Resistance($R$)
- Capacitor with Inverse of Capacitance($1 \over C$)
- Inductor with Inductance($L$)
And, in a AC circuit, we have there voltages obtained by by multiplication with derivatives of charge($q$):
- Resistor: $V = {{dq}\over{dt}}R$
- Capacitor: $V = {q \over C}$
- Inductor: $V = {{d^2q}\over{dt^2}}L$
Well, let's limit our talk to only AC circuits, with $sine$ and $cosine$ type currents only..
The main question:
If there existed some device like antiresistor (infracapacitor or ultrainductor) ($P_C$ or $P_I$) or so, in which potential drops in direction opposite to current or more specifically, either (ultrainductor) $$V = {{d^3q}\over{dt^3}}P_I$$ (infracapacitor) or $$V = P_C\int{q \times dt}$$So, for a circuit with current in $sine$ and $cosine$ wave form, the voltage would have obviously dropped in opposite direction of current. Now, as at resonance, voltage of Inductor cancels the voltage of Capacitor, probably here this so-called antiresistor may cancel voltage of resistor. Probably, giving some awkward but seemingly useful condition.
My question is, is this type device possible (from simple wires, plates etc. or from semiconductor etc. or from some quantum phenomenon)?
Or, even if it doesn't exist, am I thinking correct for a hypothetical resonance?
Explanation:
if $i = i_0 \sin{wt}$, charge will be $−{i_0 \over w}\cos{wt}$, and potential across the device will be either $$−P_Ii_0w^2\sin{wt}$$ or $$−P_C{i_0 \over w^2}\sin{wt}$$ from the equations and for resistor $Ri_0\sin{wt}$, which are opposite.
@resonance
- ultrainductor: $R=P_Iw^2$ or $w=\sqrt{R \over P_I}$
- infracapacitor: $R={P_C \over w^2}$ or $w=\sqrt{P_C \over R}$
I changed characteristic property of capacitor from $C$ to $1 \over C$ in my question, for obvious reasons. And, now the resonance of capacitor and inductor becomes:
$w = \sqrt{1 \over {LC}} = \sqrt{({\frac{1}{C}}) \over L}$
which is again similar to our hypothetical resonance.
