Video Transcript
A circuit consists of a resistor, a capacitor, and an inductor, all of which are in series. An alternating voltage source is connected to the circuit and an alternating current is generated. How does the resonant frequency of the circuit change if the resistance of the resistor is increased? (A) The resonant frequency increases. (B) The resonant frequency decreases. (C) The resonant frequency does not change.
In this example, we have a circuit with a resistor, a capacitor, and an inductor as well as an alternating voltage supply. We’re told that the resistance of the resistor in this circuit is increased, and we want to know what effect that has on the resonant frequency of the circuit. In general, the frequency of an alternating current circuit is the frequency at which the current or equivalently the voltage oscillates.
Of all possible frequency values, there’s one called the resonant frequency; we’ll refer to it as 𝑓 sub R. This frequency is the frequency at which current in the circuit can oscillate so as to minimize the overall opposition to charge flow. Mathematically, the resonant frequency is determined by this relationship. Notice that the only two variables on the right-hand side are the inductance 𝐿 and the capacitance 𝐶. In other words, the resonant frequency of a circuit does not depend on the resistance 𝑅 of that circuit. That resistance finds no place in this equation. This tells us that even if the resistance of our resistor were increased, that by itself would not change the resonant frequency of the circuit. That frequency depends on inductance and capacitance, but not on resistance. We choose answer option (C).
