### 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 capacitance of the capacitor is increased? (A) The resonant frequency
increases. (B) The resonant frequency
decreases. (C) The resonant frequency does not
change.

Here, weβre told that our circuit
consists of a resistor, a capacitor, and an inductor. And thereβs an alternating voltage
supply. This supply will vary the voltage
with some frequency. And it may be at what is called the
resonant frequency of the circuit. If we symbolize the resonant
frequency as π sub π, we can recall that mathematically π sub π is one over two
π times the square root of π times π. Here, π is the value of our
inductor and π is the capacitance of our capacitor.

In this example, weβre to imagine
that the capacitance of the capacitor increases. We want to know what effect will
that increase have on the resonant frequency of the circuit. Looking at our mathematical
expression for resonant frequency, we see that if a value in the denominator, the
capacitance, gets larger, then if nothing else changes, this fraction overall will
decrease. That is, if capacitance π
increases, then π sub π, the resonant frequency, decreases. This is indicated by answer option
(B). In this circuit, if the capacitance
of the capacitor is increased, the resonant frequency decreases.