Video Transcript
Fill in the blank: In a series circuit containing a resistor, a capacitor, and an inductor, the resonant frequency of the circuit is the frequency of the circuit when its impedance has its blank value. (A) Maximum, (B) minimum, (C) mean, (D) root mean square.
Let’s say that this is the circuit we’re working with, with an alternating current supply and a resistor, a capacitor, and an inductor in series. Current as well as voltage is provided to this circuit at some frequency. This frequency can be tuned so that it matches up with the rest of the circuit components. In particular, the frequency can be set depending on the inductance of the inductor 𝐿 and the capacitance of the capacitor 𝐶. The idea behind setting the frequency of this circuit at just the right frequency, called the resonant frequency, is to minimize the circuit’s overall opposition to the flow of charge. This overall opposition is called the circuit’s impedance. When an impedance is high, it’s harder for charge to flow, and when it’s low, it is easier.
For a more efficient circuit then, one where charge flows more easily, we want impedance to be low. Impedance depends on the frequency in the circuit. So we can intentionally set that frequency so that impedance is at its lowest, that is, its minimum value. When we do this, we aid the flow of charge in this circuit as much as possible given the values of our other circuit components: the resistor, the inductor, and the capacitor.
Our completed sentence reads in a series circuit containing a resistor, a capacitor, and an inductor, the resonant frequency of the circuit is the frequency of the circuit when its impedance has its minimum value. We choose answer option (B).