Question 6A86

When a capacitor and an inductor with equal values of reactance are connected in parallel, the circuit is at parallel resonance. At resonance, the inductive current ($I_L$) and the capacitive current ($I_C$) are equal in magnitude but flow 180 degrees out of phase with each other. These currents effectively cancel each other out in the external circuit. Because the reactive currents cancel, the total current drawn from the source is theoretically zero (assuming ideal components). According to Ohm's Law ($Z = V/I$), if the current ($I$) approaches zero, the total impedance ($Z$) approaches infinity. Furthermore, since the reactive components perfectly cancel, the circuit presents zero net reactance to the source. Any impedance at this point would be purely resistive, hence "resistive and infinite" for an ideal circuit. Therefore, the total reactance is zero, and the total impedance is infinite and purely resistive.