Electrical Circuits

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 ( ) and the reactance of the capacitor ( ) are equal. Here, is the angular frequency, where is the frequency of the applied AC. At resonance, the inductive reactance ( ) cancels out the capacitive reactance ( ), making the total impedance of the circuit very low. As a result, the current in the circuit becomes maximum.
The resonance frequency is given by the formula: where is the inductance and 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.

Step 1: Understanding series circuit.
In a series circuit, the current that flows through all the resistors is the same because the current has only one path to follow. The total current flowing through the circuit is the same at every point in a series configuration.
Step 2: Explanation of each option.
- (A) same: Correct. In a series circuit, the current through each resistor is the same.
- (B) different: Incorrect. The current is the same throughout the series circuit.
- (C) zero: Incorrect. The current is not zero unless the circuit is open.
- (D) divided proportionally to the value of resistance: Incorrect. This statement is true for parallel circuits, not series circuits.
Step 3: Conclusion.
The current flowing through each resistor in a series circuit is the same.