Question

Explain electrical resonance.

Hint:

\textbf{Electrical resonance} = Maximum energy transfer occurs when the applied frequency equals the circuit's natural frequency. In series circuits, this leads to maximum current; in parallel circuits, to minimum impedance.

Answer 1

Electrical resonance refers to the phenomenon that occurs in an electrical circuit when the frequency of the applied alternating current (AC) matches the natural frequency of the circuit, leading to the maximum transfer of energy between the circuit components. This is especially significant in circuits containing inductors (L) and capacitors (C), commonly known as LC circuits. Resonance can be observed in both series and parallel LC circuits, but the effects differ.
1. Resonance in Series LC Circuit: In a series LC circuit, resonance occurs when the reactance of the inductor (\(X_L = \omega L\)) and the reactance of the capacitor (\(X_C = \frac{1}{\omega C}\)) are equal. Here, \(\omega = 2 \pi f\) is the angular frequency, where \(f\) is the frequency of the applied AC. At resonance, the inductive reactance (\(X_L\)) cancels out the capacitive reactance (\(X_C\)), making the total impedance of the circuit very low. As a result, the current in the circuit becomes maximum.
The resonance frequency \(f_0\) is given by the formula: \[ f_0 = \frac{1}{2 \pi \sqrt{LC}} \] where \(L\) is the inductance and \(C\) is the capacitance. At this frequency, the energy oscillates between the magnetic field of the inductor and the electric field of the capacitor.
2. Resonance in Parallel LC Circuit: In a parallel LC circuit, resonance occurs when the impedance of the circuit becomes infinite, and the current through the circuit becomes minimal. The parallel LC circuit exhibits a different kind of behavior compared to the series circuit, but the concept of resonance remains the same—the total reactance of the circuit becomes zero at the resonance frequency.
3. Application of Electrical Resonance: Electrical resonance is crucial in many applications, such as:
- Tuned circuits in radio receivers, where a circuit resonates at a particular frequency to select a desired signal.
- Filter circuits, where resonance can be used to select or block certain frequencies.
- Transformers and inductive coils in power systems use resonance to maximize energy efficiency.
In conclusion, electrical resonance occurs when the frequency of an applied AC voltage matches the natural frequency of a circuit, resulting in maximum energy transfer in series circuits and minimum impedance in parallel circuits. This phenomenon is fundamental to various electrical and electronic devices.