Which of the following statements is NOT correct regarding resonance in a series circuit?

Explanation:

Resonance in a Series Circuit

Definition: Resonance in an electrical series circuit occurs when the inductive reactance (XL) is equal to the capacitive reactance (XC), resulting in their effects canceling each other out. This leads to a purely resistive circuit where the impedance is minimized and is equal to the resistance of the circuit. At resonance, the circuit oscillates at its natural frequency, which is determined by the inductance (L) and capacitance (C) in the circuit.

Correct Option Analysis:

The correct option is:

Option 4: The phase angle of the circuit is 90°.

This option is NOT correct because, at resonance in a series circuit, the phase angle between the voltage and current is 0°, not 90°. At resonance, the inductive and capacitive reactances cancel each other out, and the circuit behaves as a purely resistive circuit. In a purely resistive circuit, the voltage and current are in phase, meaning the phase angle is 0°. A phase angle of 90° would indicate a completely reactive circuit (either purely inductive or purely capacitive), which is not the case at resonance in a series circuit.

Important Information: At resonance, the following conditions are observed:

• Inductive reactance (XL) = Capacitive reactance (XC).
• The impedance of the circuit is equal to the resistance (Z = R).
• The circuit behaves as a purely resistive circuit, with no reactive component.
• The current is at its maximum value, as the impedance is minimized.
• The voltage across the inductor and capacitor is equal in magnitude but opposite in phase, effectively canceling each other out.

Additional Information

To further understand the analysis, let’s evaluate the other options:

Option 1: The voltage across the capacitor and inductor is equal and opposite.

This statement is correct. At resonance, the voltage across the inductor and capacitor is equal in magnitude but opposite in phase. This means that the inductive and capacitive voltages cancel each other out, leaving only the resistive voltage in the circuit.

Option 2: The circuit behaves as a purely resistive circuit.

This statement is also correct. At resonance, the inductive and capacitive reactances cancel out, leaving only the resistive component. The impedance of the circuit is purely resistive, and the current and voltage are in phase.

Option 3: The net reactance of the circuit is zero.

This statement is correct as well. At resonance, the inductive reactance (XL) is equal to the capacitive reactance (XC), resulting in a net reactance of zero. This is why the circuit behaves as a purely resistive circuit at resonance.

Option 5: [This option is not provided in the question, so no analysis is required for it.]

Conclusion:

Understanding resonance in a series circuit is crucial for analyzing the behavior of electrical circuits at specific frequencies. At resonance, the circuit achieves unique characteristics such as maximum current flow, zero net reactance, and purely resistive behavior. While most statements provided in the options align with the principles of resonance, the incorrect statement is Option 4, as the phase angle of a resonant series circuit is 0° and not 90°.