often it is highly desirable to minimize the impedance in a circuit. if the circuit contains a resistor, a capacitor, and an inductor, where the resistor and capacitor must be R and C respectively, and the inductor may have any value, what is the minimum impedance possible for the circuit?

minimum impedance? Silly question. Is it a parallel circuit...if so, minimum impedance is at f=0, and impedance is equal to the resistance of the inductor. At f= extremely high, impedance is again zero, due to the zero capacitive reactance.

If a series circuit, and f is at resonant frequency, impedance is R at the minimum.