The book I am reading does not go into greater detail of what Resonance within a circuit really is. The only definition I am given is that of the Resonant Angular Frequency. Which is the angular frequency for maximum oscillation.
$$\omega L= \frac{1}{\omega C}
$$
$$ \omega_0 = \frac{1}{\sqrt{LC}}$$
Where L is Inductance and C is capacitance. I can see here that the resonance depends on the values for capacitance and inductor's.
From the definition alone, I'd guess that it'd mean the frequency at which you're getting a maximum current when ever the maximum electro-motive force is held constant.
$$I = \frac{E}{Z} $$Where Z is the impedance of the RLC circuit. And E is EMF max.
So… the current is at it's max when the Inductance and Capacitance are both zero. I'd guess that this would mean that a circuit would be seen as if only the Resistors are in effect.
But what does this conceptually imply? And when would it matter in use?
Best Answer
You are incorrect when you say "... the current is at it's max when the Inductance and Capacitance are both zero." If the capacitance were zero, the effect would be that you have a break in the circuit and no current would flow. If the voltage across the circuit is $V(t) = V_0 \sin(\omega t)$ then for an RLC series circuit the current through the circuit is given as $$I(t) = \frac{V_0}{|Z|} \sin (\omega t - \phi)$$ where the impedance, $Z$, is given as $Z = \sqrt{R^2 + (X_L - X_C)^2}$, with $X_L = \omega L, X_C = \frac{1}{\omega C}$ and $\phi$ is the phase between the current and the applied voltage. For given vales of $R, L, C$ and varying $\omega$, this has a minimum value of $R$ when $X_L = X_C$ meaning a maximum current will flow. You can determine the resonant frequency from $\omega_0 L = \frac{1}{\omega_0 C}$.