Final answer:
The complex impedance of a parallel LC circuit can be calculated using the individual inductive and capacitive reactances and combining them inversely. This impedance reaches a minimum at the resonant frequency where the two reactances are equal and cancel out.
Step-by-step explanation:
The complex impedance of a parallel combination of an inductor (L) and a capacitor (C) can be found by calculating the individual reactances of the inductor and the capacitor and then combining them. The inductive reactance (XL) is given by XL = 2πfL, where f is the frequency and L is the inductance. The capacitive reactance (XC) is given by XC = 1/(2πfC), where C is the capacitance. The total impedance Ztotal in a parallel LC circuit is the inverse of the sum of the inverses of the individual reactances:
Ztotal = 1/((1/XL) + (1/XC)).
This total impedance will have a minimum at the resonant frequency, where XL = XC. At this frequency, the inductive and capacitive reactances cancel each other, theoretically resulting in an impedance that approaches zero, if we ignore any parasitic resistance in the circuit.