Resonance MCQ [Free PDF] – 6 Objective Questions with Answers

For a series RLC circuit, XL=XC at resonance, so the impedance is purely resistive and minimum, current is maximum, and power factor is unity. In an ideal parallel resonant circuit the input impedance is high, not minimum. Key relation: ω₀=1/√(LC); f₀=1/(2π√LC); at resonance XL=XC.

Exam focus: Series resonance: Z minimum, I maximum. Parallel resonance: input Z maximum (ideal case). Common trap: Reactive voltages can be large even though net reactive voltage is zero.

For a high-Q series RLC circuit, bandwidth is Δf = R/(2πL). With R=0.1 Ω and L=15 mH, Δf≈1.061 Hz. Half-power frequencies lie approximately symmetrically around 50 Hz, giving about 49.47 Hz and 50.53 Hz; the nearest option is 49.57 Hz and 50.53 Hz.

Electrical resonance occurs when the net reactive effect cancels. For a series RLC circuit, XL=XC at resonance, so the impedance is purely resistive and minimum, current is maximum, and power factor is unity. Key relation: ω₀=1/√(LC); f₀=1/(2π√LC); at resonance XL=XC.

Exam focus: Series resonance: Z minimum, I maximum. Parallel resonance: input Z maximum (ideal case). Common trap: Reactive voltages can be large even though net reactive voltage is zero.

A — As a purely resistive circuit. At series resonance X_L = X_C and they cancel, so Z = R (minimum) and current is maximum and in phase with voltage.

For a resonant network, bandwidth is inversely proportional to quality factor: BW = f₀/Q. Therefore a wider bandwidth requires a lower Q.

B — Q = ωL/R, with ω evaluated at resonance (ω = ω₀). The quality factor equals the voltage across either reactive component divided by the supply voltage at series resonance.