Question

Define resonant frequency of LCR series circuit.

Answer 1

Hint: We will write about series LCR circuits, how and where the energy is stored and in what form and also show analogy to physical systems and define the conditions at which the frequency is considered to be resonant to the LCR circuit and compare how this is different from a LC circuit.

Complete step by step answer:
Resonance is an important property of LCR circuits. Energy in LCR circuits can be stored in two different forms either as an electric field in a capacitor when it is charged or in an inductor as a magnetic field when current flows through it. An analogy can be drawn between the physical spring mass system and LCR circuit. The natural frequency of the spring mass system is analogous to resonance frequency in LCR circuits. At resonance frequency, the impedance of the circuit is minimum. At that frequency there will be no phase difference between the voltage and current flowing through the circuit. The value of resonance frequency is the same here as the LC circuit which is given as $\omega =\dfrac{1}{\sqrt{LC}}$. Although the value is the same there are many differences between a LC circuit and LCR circuit. The presence of resistor here makes the oscillations damped and they do not go on forever unlike for LC circuits which would not stop in ideal conditions (when there is no resistance in wires). An LCR circuit can be defined as either being underdamped or overdamped. If they are underdamped, they will resonate naturally (without a driving source) and if they do not resonate naturally, they are classified as overdamped. Their nature will only depend on the value of resistance in the circuit.

Note:
Take care not to confuse the oscillations in LC circuit and LCR circuit as same. Although their resonant frequency is the same their operations are quite different. It is very difficult to make a pure LC circuit as there will always be a little bit of resistance due to connecting wires.