Question

In LCR series resonance circuit, choose the wrong statement

• A. Resonance occurs at X_L = X_C
• B. At resonance, current has a maximum value
• C. At resonance, circuit is purely inductive
• D. At resonance, impedance is minimum

Answer 1

The Correct Option is C

Solution: Understanding Resonance in an LCR Series Circuit

An LCR series resonance circuit consists of an inductor (L), a capacitor (C), and a resistor (R) connected in series. At a specific frequency, called the resonant frequency, the circuit exhibits a unique behavior. Let's understand what happens in the circuit at resonance and why the circuit is not purely inductive.

Resonance in LCR Circuit:

At resonance, the frequency of the applied AC voltage is such that the inductive reactance (X_L) and the capacitive reactance (X_C) become equal in magnitude but opposite in sign. The inductive reactance X_L increases with frequency, while the capacitive reactance X_C decreases as frequency increases. When the two reactances cancel each other out at resonance, the impedance of the circuit becomes purely resistive.

Key Concept: Cancellation of Reactances

The key to understanding resonance is recognizing that the total reactance of the circuit is the sum of the inductive and capacitive reactances. The inductive reactance X_L is given by:

X_L = 2πfL

Where:

• f: Frequency of the AC source
• L: Inductance of the coil

On the other hand, the capacitive reactance X_C is given by:

X_C = 1 / (2πfC)

Where:

• f: Frequency of the AC source
• C: Capacitance of the capacitor

At the resonant frequency, the two reactances become equal in magnitude:

X_L = X_C

This results in the cancellation of the inductive and capacitive reactances, and the total reactance of the circuit becomes zero. As a result, the impedance of the circuit is at its minimum value, which is equal to the resistance R of the resistor.

Conclusion:

At resonance, the circuit behaves as if it is purely resistive, because the inductive and capacitive reactances cancel each other out. The circuit is no longer purely inductive or purely capacitive. Therefore, the correct statement is:

(C) At resonance, the circuit is not purely inductive.