Unit – 9 Electrical circuits and Electronics | sharpness of resonance Q factor

Sharpness of Resonance – Quality Factor (Q-Factor) | TRB Physics Notes

The sharpness of resonance of an LCR circuit indicates how selectively the circuit responds to a particular resonant frequency. This property is measured by a quantity known as the Quality Factor (Q-factor). Questions based on Q-factor are commonly asked in TRB, BRTE, and other competitive examinations.

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1. Meaning of Sharpness of Resonance

Sharpness of resonance refers to the ability of a resonant circuit to respond strongly to a narrow range of frequencies around the resonant frequency.

• High sharpness → Narrow bandwidth
• Low sharpness → Wide bandwidth

A highly sharp resonance is required in tuning circuits to select a desired signal frequency.

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2. Quality Factor (Q-Factor)

The quality factor (Q) is a dimensionless quantity that represents the sharpness of resonance of an LCR circuit.

Definition:

Q = Resonant frequency / Bandwidth

Q = f₀ / BW

For Series LCR Circuit

Q = (1 / R) × √(L / C)

For Parallel LCR Circuit

Q = R × √(C / L)

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3. Bandwidth (BW)

Bandwidth is defined as the difference between the upper and lower half-power frequencies.

BW = f₂ − f₁

At half-power frequencies, the power becomes half of the maximum value.

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4. Relation Between Q-Factor and Sharpness

• Q ∝ Sharpness of resonance
• High Q → High selectivity
• High Q → Low energy loss
• High Q → Narrow bandwidth

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5. Effect of Resistance on Q-Factor

• In series LCR circuit:
  • Q is inversely proportional to R
  • Increase in R → Decrease in Q
• In parallel LCR circuit:
  • Q is directly proportional to R
  • Increase in R → Increase in Q

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6. Shortcut Tricks for TRB Exams

• High Q → Sharp resonance
• Low Q → Flat resonance
• BW small → Q large
• BW large → Q small
• Series circuit: R ↑ → Q ↓
• Parallel circuit: R ↑ → Q ↑

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7. Comparison Table: High Q vs Low Q

Feature	High Q Circuit	Low Q Circuit
Sharpness of resonance	High	Low
Bandwidth	Narrow	Wide
Selectivity	High	Low
Energy loss	Low	High
Application	Tuning circuits	Audio amplifiers

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8. TRB Level MCQs (10 Questions)

1. Sharpness of resonance is measured by:
   (A) Bandwidth
   (B) Power
   (C) Quality factor
   (D) Impedance
   Answer: (C)
2. Quality factor is defined as:
   (A) BW / f₀
   (B) f₀ / BW
   (C) R / L
   (D) L / R
   Answer: (B)
3. High Q-factor indicates:
   (A) Wide bandwidth
   (B) Low selectivity
   (C) Sharp resonance
   (D) High power loss
   Answer: (C)
4. If bandwidth increases, Q-factor:
   (A) Increases
   (B) Decreases
   (C) Remains same
   (D) Becomes zero
   Answer: (B)
5. In a series LCR circuit, Q-factor depends on:
   (A) R only
   (B) L only
   (C) C only
   (D) R, L, and C
   Answer: (D)
6. Unit of quality factor is:
   (A) Ohm
   (B) Hertz
   (C) Henry
   (D) No unit
   Answer: (D)
7. Quality factor is maximum when:
   (A) Resistance is large
   (B) Resistance is small
   (C) Capacitance is zero
   (D) Inductance is zero
   Answer: (B)
8. Q-factor is directly proportional to:
   (A) Bandwidth
   (B) Resistance
   (C) Sharpness
   (D) Power loss
   Answer: (C)
9. Which circuit requires high Q-factor?
   (A) Power supply
   (B) Rectifier
   (C) Tuning circuit
   (D) Heater
   Answer: (C)
10. Bandwidth is minimum when:
    (A) Q is maximum
    (B) Q is minimum
    (C) R is large
    (D) L is zero
    Answer: (A)

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Exam Tip: In TRB exams, Q-factor questions are mostly direct. Remember the relation between Q, bandwidth, and resistance.