What condition characterizes electrical resonance in a series LCR circuit connected to an AC voltage source of variable angular frequency ω?
Answer and explanation
Correct answer: A. ω = 1/√(LC), where impedance Z = R is minimum and current is maximum
- Step 1: In a series LCR circuit, the impedance is .
- Step 2: Resonance occurs when the net reactance vanishes: .
- Step 3: Solving for resonant angular frequency: .
- Step 4: At this resonant frequency, , so the impedance reduces to its minimum possible value .
- Step 5: Consequently, the current amplitude reaches its maximum, and current is strictly in phase with applied voltage (power factor ).
Answer
ω = 1/√(LC), where impedance Z = R is minimum and current is maximum
Why not the others: 'ω = √(LC)' inverts the fractional formula; 'ω = 1/(LC)' forgets the square root; 'ω = R/L' represents the reciprocal of the inductive time constant rather than resonance.
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