Why this topic is important for ECET?
Resonance is one of the most scoring topics in ECET EEE. Many questions come directly from series and parallel resonance circuits, focusing on resonance frequency, bandwidth, and quality factor. If you master this, you can easily secure 2–3 marks in exams. It also connects to communication circuits, filters, and power systems.
📘 Concept Notes
1. What is Resonance?
Resonance occurs in an AC circuit when the inductive reactance (XL) equals the capacitive reactance (XC). At this point, the circuit impedance is purely resistive, and current is maximum in series resonance (or voltage is maximum across elements in parallel resonance).
Condition for resonance:
Since:
Resonance angular frequency:
Resonance frequency:
2. Series Resonance (RLC Series Circuit)
- Current is maximum at resonance.
- Impedance is minimum =
. - Power factor = 1 (unity).
3. Parallel Resonance (Tank Circuit)
- Current drawn from the supply is minimum at resonance.
- Impedance is maximum.
- Used in filters, oscillators, and communication systems.
4. Bandwidth and Quality Factor (Q-Factor)
- Bandwidth (BW):
where
= lower and upper half-power frequencies. - Quality Factor (Q):
High Q → Narrow bandwidth (sharp resonance).
5. Applications of Resonance
- Tuning radio/TV receivers.
- Induction heating.
- Power factor correction.
- Oscillators and filters.
⚙️ Formulas
- Inductive reactance:
- Capacitive reactance:
- Resonance angular frequency:
- Resonance frequency:
- Bandwidth:
- Q-Factor:
🔟 10 MCQs
Q1. In a series RLC circuit, resonance occurs when:
a) 
b)
c) 
d) None
Q2. Resonance frequency is given by:
a) 
b) 
c) 
d) None
Q3. At resonance, the impedance of a series RLC circuit is:
a) 
b) 
c) 
d) Infinite
Q4. At resonance, the power factor of a series RLC circuit is:
a) Zero
b) Unity
c) Lagging
d) Leading
Q5. In parallel resonance, current drawn from supply is:
a) Maximum
b) Minimum
c) Zero
d) Infinite
Q6. A series RLC circuit has 
. Find resonance frequency.
a) 15.9 Hz
b) 50.3 Hz
c) 159 Hz
d) 503 Hz
Q7. A circuit has 
. Find Q.
a) 5
b) 10
c) 20
d) None
Q8. Bandwidth of a series RLC circuit is inversely proportional to:
a) Resistance
b) Capacitance
c) Inductance
d) Quality factor
Q9. Resonance is used in:
a) Filters
b) Oscillators
c) Tuned amplifiers
d) All
Q10. At resonance, the reactive power in a series RLC circuit is:
a) Maximum
b) Zero
c) Infinite
d) Negative
✅ Answer Key
| Q.No | Answer |
|---|---|
| 1 | b |
| 2 | b |
| 3 | a |
| 4 | b |
| 5 | b |
| 6 | c |
| 7 | c |
| 8 | a |
| 9 | d |
| 10 | b |
🧠 Explanations
- Q1: Resonance → → (b).
- Q2: Formula: → (b).
- Q3: At resonance, net reactance cancels → → (a).
- Q4: Power factor = 1 at resonance → (b).
- Q5: In parallel resonance, supply current is minimum → (b).
- Q6:
→ (c). - Q7:
→ (c). - Q8: Bandwidth
→ inversely proportional to → (a). - Q9: Resonance is used in all mentioned → (d).
- Q10: At resonance, reactive powers cancel → net = 0 → (b).
🎯 Motivation / Why Practice Matters
Resonance is a high-frequency question topic in ECET 2026. Many students make mistakes with formulas like 
and 
. Practicing problems improves calculation speed and accuracy, which is crucial under exam time pressure. A small mistake in frequency calculation can cost valuable marks — so daily practice is your competitive edge.
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