Question

Define resonant frequency of LCR circuit.

Answer 1

Hint: The transfer function will get its maximum value at a certain frequency. That is, for a given input, the maximum output will be obtained in the circuit. At this point capacitive reactance of the capacitor becomes equal in value to the inductive reactance of the inductor.

Complete step by step solution:
Let’s discuss about the LCR circuits first:
An RLC circuit is an electrical circuit which consists of a capacitor, an inductor, and a resistor connected in parallel or in series. The name is derived from the letters which are used to denote the constituent components used in this circuit, but the sequence of the components in the circuit may vary from LCR.
In an electrical system, the transfer function will get its maximum value at a certain frequency. This frequency is known as the resonant frequency of that circuit. Thus for a given input, the maximum output can be obtained in the circuit. It has been proved that the resonance is obtained when the inductive impedance and capacitive impedance values are equal. Let us begin an interesting topic!
In a LCR circuit there becomes a frequency point at which capacitive reactance of the capacitor becomes equal in value to the inductive reactance of the inductor.
In other words, $X_C=X_L$
(Reactance is a property that opposes a change in current and is found in both inductors and capacitors)
The point at which this phenomenon occurs is called the Resonant Frequency point.
Resonance Frequency is given by, $f_r={\displaystyle \frac{1}{2\pi \sqrt{LC}}}$
Where, $C$ is the capacitance
$L$ is the inductance

Note: Electrical resonance occurs in a circuit at a particular resonant frequency when the impedances cancel each other. In some circuits, this happens when the impedance between the output and input of the circuit is almost zero and the transfer function is close to one. The voltage across the inductor leads the current and the voltage across the capacitor lags the current.