Amateur Extra E5A: Resonance and Q
These are the 13 official questions in group E5A of the 2024–2028 Amateur Extra question pool, with the correct answer marked and a plain-English explanation of why it's right. The real exam asks one question from this group.
- E5A01Question 1
What can cause the voltage across reactances in a series RLC circuit to be higher than the voltage applied to the entire circuit?
- AResonance Correct
- BCapacitance
- CLow quality factor (Q)
- DResistance
Why: At resonance, the voltage across each reactance can exceed the applied voltage.
- E5A02Question 2
What is the resonant frequency of an RLC circuit if R is 22 ohms, L is 50 microhenries, and C is 40 picofarads?
- A44.72 MHz
- B22.36 MHz
- C3.56 MHz Correct
- D1.78 MHz
Why: f = 1 ÷ (2π√(50 µH × 40 pF)) ≈ 3.56 MHz.
- E5A03Question 3
What is the magnitude of the impedance of a series RLC circuit at resonance?
- AHigh, compared to the circuit resistance
- BApproximately equal to capacitive reactance
- CApproximately equal to inductive reactance
- DApproximately equal to circuit resistance Correct
Why: At series resonance the reactances cancel, leaving about the resistance.
- E5A04Question 4
What is the magnitude of the impedance of a parallel RLC circuit at resonance?
- AApproximately equal to circuit resistance Correct
- BApproximately equal to inductive reactance
- CLow compared to the circuit resistance
- DHigh compared to the circuit resistance
Why: At parallel resonance the impedance is also about equal to the resistance.
- E5A05Question 5
What is the result of increasing the Q of an impedance-matching circuit?
- AMatching bandwidth is decreased Correct
- BMatching bandwidth is increased
- CLosses increase
- DHarmonics increase
Why: Higher Q narrows the matching bandwidth.
- E5A06Question 6
What is the magnitude of the circulating current within the components of a parallel LC circuit at resonance?
- AIt is at a minimum
- BIt is at a maximum Correct
- CIt equals 1 divided by the quantity 2 times pi, times the square root of (inductance L multiplied by capacitance C)
- DIt equals 2 times pi, times the square root of (inductance L multiplied by capacitance C)
Why: Circulating current inside a parallel LC circuit is at a maximum at resonance.
- E5A07Question 7
What is the magnitude of the current at the input of a parallel RLC circuit at resonance?
- AMinimum Correct
- BMaximum
- CR/L
- DL/R
Why: The input current to a parallel RLC circuit is at a minimum at resonance.
- E5A08Question 8
What is the phase relationship between the current through and the voltage across a series resonant circuit at resonance?
- AThe voltage leads the current by 90 degrees
- BThe current leads the voltage by 90 degrees
- CThe voltage and current are in phase Correct
- DThe voltage and current are 180 degrees out of phase
Why: At series resonance, voltage and current are in phase.
- E5A09Question 9
How is the Q of an RLC parallel resonant circuit calculated?
- AReactance of either the inductance or capacitance divided by the resistance
- BReactance of either the inductance or capacitance multiplied by the resistance
- CResistance divided by the reactance of either the inductance or capacitance Correct
- DReactance of the inductance multiplied by the reactance of the capacitance
Why: Parallel Q = R ÷ X (either reactance).
- E5A10Question 10
What is the resonant frequency of an RLC circuit if R is 33 ohms, L is 50 microhenries, and C is 10 picofarads?
- A7.12 MHz Correct
- B23.5 kHz
- C7.12 kHz
- D23.5 MHz
Why: f = 1 ÷ (2π√(50 µH × 10 pF)) ≈ 7.12 MHz.
- E5A11Question 11
What is the half-power bandwidth of a resonant circuit that has a resonant frequency of 7.1 MHz and a Q of 150?
- A157.8 Hz
- B315.6 Hz
- C47.3 kHz Correct
- D23.67 kHz
Why: 7.1 MHz ÷ 150 ≈ 47.3 kHz.
- E5A12Question 12
What is the half-power bandwidth of a resonant circuit that has a resonant frequency of 3.7 MHz and a Q of 118?
- A436.6 kHz
- B218.3 kHz
- C31.4 kHz Correct
- D15.7 kHz
Why: 3.7 MHz ÷ 118 ≈ 31.4 kHz.
- E5A13Question 13
What is an effect of increasing Q in a series resonant circuit?
- AFewer components are needed for the same performance
- BParasitic effects are minimized
- CInternal voltages increase Correct
- DPhase shift can become uncontrolled
Why: Higher Q in a series resonant circuit increases its internal voltages.