Question

How do you calculate the resonant frequency of an RC circuit?

Answer 1

To calculate the resonant frequency of an RC circuit, you need to consider the components of the circuit: a resistor (R) and a capacitor (C). The resonant frequency is the frequency at which the capacitive reactance (Xc) and the resistive impedance (R) are equal. At this frequency, the impedance of the circuit becomes purely resistive, and the circuit exhibits maximum response to AC signals.

The capacitive reactance (Xc) of a capacitor in an AC circuit is given by:

Xc = 1 / (2πfC)

Where:
Xc = Capacitive reactance in ohms (Ω)
f = Frequency in hertz (Hz)
C = Capacitance of the capacitor in farads (F)

The resistive impedance (R) of the resistor in the circuit is simply the resistance value (R) in ohms (Ω).

To find the resonant frequency, you set Xc equal to R and solve for f:

1 / (2πfC) = R

Now, rearrange the equation to solve for f:

f = 1 / (2πRC)

Now that you have the formula for the resonant frequency (f), you can plug in the values of R and C from your circuit to calculate the resonant frequency. The unit of capacitance (C) should be in farads (F), and the resistance (R) should be in ohms (Ω).

Keep in mind that the resonant frequency of an RC circuit is only valid in a sinusoidal AC circuit with a steady-state response. For other types of waveforms or transient behavior, the concept of resonant frequency may not apply in the same way.