Question E5A13:
What is an effect of increasing Q in a series resonant circuit?  

Choices:  
A: Fewer components are needed for the same performance  
B: Parasitic effects are minimized  
C: Internal voltages increase  
D: Phase shift can become uncontrolled    

Correct Answer is  C: Internal voltages increase  

Correct answer: C — Internal voltages increase

Why this is correct:
- In a series-resonant RLC, the impedance at resonance is minimum and equals the series resistance, $Z_\text{res} \approx R$, so the current is high: $I_\text{res} = V/R$.
- The quality factor (for series resonance) is $Q = \dfrac{\omega_0 L}{R} = \dfrac{1}{\omega_0 C R}$.
- At resonance, the reactive voltages are:
  $$V_L = I_\text{res} X_L,\quad V_C = I_\text{res} X_C$$
  and since $X_L = X_C$ in magnitude at resonance,
  $$V_L = V_C \approx Q \cdot V_\text{source}.$$
- Thus, as $Q$ increases, the internal voltages across L and C increase proportionally (voltage magnification).

Why the other choices are incorrect:
- A: Fewer components are needed for the same performance  
  Q has nothing to do with the number of components; it’s a measure of damping/selectivity in the given circuit.
- B: Parasitic effects are minimized  
  Higher Q makes the circuit more sensitive to small parasitics, not less. Parasitic R/L/C can detune or lower Q more noticeably.
- D: Phase shift can become uncontrolled  
  In a series-resonant circuit, the net phase at resonance is 0 degrees. Higher Q sharpens the phase-vs-frequency transition but does not make it “uncontrolled.”

Useful formulas and rules of thumb:
- Series-resonant Q:
  $$Q = \frac{\omega_0 L}{R} = \frac{1}{\omega_0 C R}$$
- Resonant current:
  $$I_\text{res} = \frac{V_\text{source}}{R} = \frac{V_\text{source} \, Q}{X_L}$$
- Voltage magnification across L or C at resonance:
  $$V_L \approx V_C \approx Q \cdot V_\text{source}$$
- Bandwidth (half-power):
  $$\text{BW} \approx \frac{f_0}{Q}$$

Tip: High-Q series circuits can have very large internal voltages; ensure component voltage ratings are adequate.