Day 13 ECET 2026 ECE – Resonance in Circuit Theory

Why this topic is important for ECET?

Resonance is one of the most important topics in Circuit Theory. In ECET, both conceptual and numerical problems are often asked from this area. Resonance is directly applied in communication circuits, filters, oscillators, and antennas. If you master resonance, you can solve questions quickly in exams and secure easy marks.

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📘 Concept Notes

1. What is Resonance?

• Resonance occurs in an AC circuit when the inductive reactance equals the capacitive reactance.
• At this condition, the circuit allows maximum current (in series) or maximum/minimum impedance (in parallel).

Where:

• 
• 

At resonance:

So, the resonant frequency is:

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2. Types of Resonance

(a) Series Resonance

• Occurs in a series RLC circuit.
• At resonance:
  • Impedance = (minimum).
  • Current is maximum.
  • Power factor = 1 (unity).

Application: Tuning circuits in radios and communication systems.

(b) Parallel Resonance (Tank Circuit)

• Occurs in a parallel RLC circuit.
• At resonance:
  • Impedance is maximum.
  • Current drawn from source is minimum.

Application: Oscillators, filters, antenna circuits.

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3. Quality Factor (Q)

• Q defines sharpness of resonance.
• Higher Q → Narrow bandwidth, better selectivity.

For series circuit:

Bandwidth:

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4. Example

A series RLC circuit has L = 1 mH, C = 10 μF, R = 10 Ω. Find resonant frequency.

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⚙️ Formulas

• Inductive reactance:
• Capacitive reactance:
• Resonant frequency:
• Impedance at resonance (series):
• Current at resonance (series):
• Q factor:
• Bandwidth:
• Power factor at resonance:

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🔟 10 MCQs

Q1. In a series RLC circuit, resonance occurs when:
a)
b)
c)
d)

Q2. Resonant frequency of an RLC circuit is given by:
a)
b)
c)
d)

Q3. In series resonance, impedance is:
a) Maximum
b) Minimum
c) Zero
d) Infinite

Q4. In parallel resonance, impedance is:
a) Minimum
b) Maximum
c) Zero
d) Equal to R

Q5. A series circuit has R = 20 Ω, L = 0.2 H, C = 100 μF. Find resonant frequency.

Q6. For a series resonant circuit, Q factor is given by:
a)
b)
c)
d)

Q7. Bandwidth of a resonant circuit is related to Q by:
a)
b)
c)
d)

Q8. If Q = 50 and f0 = 10 kHz, find BW.

Q9. In resonance, power factor is:
a) 0
b) 0.5
c) 1
d) Depends on circuit

Q10. Parallel resonance circuits are widely used in:
a) Rectifiers
b) Oscillators
c) Transformers
d) Motors

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✅ Answer Key

Q No	Answer
Q1	c
Q2	a
Q3	b
Q4	b
Q5	35.6 Hz
Q6	a
Q7	c
Q8	200 Hz
Q9	c
Q10	b

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🧠 Explanations

• Q1: Resonance when .
• Q2: Standard formula for resonance frequency.
• Q3: At resonance, Z = R (minimum).
• Q4: In parallel resonance, Z is maximum.
• Q5: .
• Q6: Q = .
• Q7: Bandwidth = .
• Q8: BW = .
• Q9: Power factor at resonance is 1.
• Q10: Parallel resonance (tank circuit) is used in oscillators.

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🎯 Motivation / Why Practice Matters

Resonance problems are direct and formula-based in ECET, making them high-scoring questions.

• Solving more problems increases speed in applying formulas.
• Mastery helps in both core ECE subjects and advanced communication systems.
• A strong grip here ensures you don’t lose marks on easy but tricky numerical questions.

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