Unit – 9 Electrical circuits and Electronics | series and parallel resonant-LCR circuits

Series and Parallel Resonant LCR Circuits – TRB Competitive Exam Notes

Resonance is an important concept in AC circuits involving resistance (R), inductance (L), and capacitance (C). Questions on series and parallel resonant LCR circuits are frequently asked in TRB, BRTE, and other Tamil Nadu competitive examinations.

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1. Series Resonant LCR Circuit

A series LCR circuit consists of a resistor, an inductor, and a capacitor connected in series with an AC supply.

Condition for Resonance

Resonance occurs when inductive reactance equals capacitive reactance.

X_L = X_C

2πf₀L = 1 / (2πf₀C)

Resonant Frequency:

f₀ = 1 / (2π√(LC))

Impedance at Resonance

At resonance, impedance is minimum and equal to resistance.

Z = R

Current at Resonance

Current is maximum at resonance.

Phase Relation

At resonance, current and voltage are in phase.

Power Factor

Power factor = 1 (Unity)

Important TRB Points

• Impedance is minimum
• Current is maximum
• Circuit behaves like pure resistance
• Used in tuning circuits (radio, TV)

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2. Parallel Resonant LCR Circuit

A parallel LCR circuit consists of an inductor and a capacitor connected in parallel with resistance.

Condition for Resonance

Resonance occurs when net reactance becomes zero.

Resonant Frequency:

f₀ = 1 / (2π√(LC))

Impedance at Resonance

At resonance, impedance is maximum.

Current at Resonance

Line current drawn from the source is minimum.

Phase Relation

Supply current is in phase with voltage.

Important TRB Points

• Impedance is maximum
• Current drawn is minimum
• Also called rejector circuit
• Used in filter circuits

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3. Bandwidth and Quality Factor

Bandwidth (BW)

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

BW = f₂ − f₁

Quality Factor (Q)

Quality factor indicates sharpness of resonance.

Q = f₀ / BW

Higher Q → Sharper resonance

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4. Shortcut Tricks for TRB Exams

• Series resonance → Z minimum → I maximum
• Parallel resonance → Z maximum → I minimum
• At resonance: XL = XC
• Resonant frequency formula is SAME for series and parallel circuits
• Series → Acceptor circuit
• Parallel → Rejector circuit
• Power factor at resonance = 1

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5. Comparison Table: Series vs Parallel Resonant Circuit

Feature	Series Resonant LCR	Parallel Resonant LCR
Impedance at resonance	Minimum	Maximum
Current at resonance	Maximum	Minimum
Power factor	Unity	Unity
Nature of circuit	Purely resistive	Purely resistive
Alternate name	Acceptor circuit	Rejector circuit
Main application	Tuning circuits	Filter circuits

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6. TRB Level MCQs (10 Questions)

1. Resonance occurs when:
   (A) XL > XC
   (B) XL < XC
   (C) XL = XC
   (D) R = 0
   Answer: (C)
2. Impedance of series LCR circuit at resonance is:
   (A) Maximum
   (B) Minimum
   (C) Zero
   (D) Infinite
   Answer: (B)
3. Current in a series resonant circuit at resonance is:
   (A) Minimum
   (B) Zero
   (C) Maximum
   (D) Constant
   Answer: (C)
4. Parallel resonance circuit is also called:
   (A) Acceptor circuit
   (B) Amplifier
   (C) Rejector circuit
   (D) Rectifier
   Answer: (C)
5. Power factor at resonance is:
   (A) Zero
   (B) Less than 1
   (C) Greater than 1
   (D) Unity
   Answer: (D)
6. Resonant frequency depends on:
   (A) R only
   (B) L and C only
   (C) R and L
   (D) R and C
   Answer: (B)
7. Bandwidth is related to:
   (A) Impedance
   (B) Current
   (C) Quality factor
   (D) Voltage
   Answer: (C)
8. Quality factor is maximum when:
   (A) Bandwidth is large
   (B) Bandwidth is small
   (C) Frequency is zero
   (D) Resistance is zero
   Answer: (B)
9. At resonance, phase angle between V and I is:
   (A) 90°
   (B) 45°
   (C) 180°
   (D) 0°
   Answer: (D)
10. Which circuit draws minimum current at resonance?
    (A) Series LCR
    (B) R–L
    (C) Parallel LCR
    (D) R–C
    Answer: (C)

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Exam Tip: In TRB exams, resonance questions are usually direct formula-based. Remember minimum–maximum rules and acceptor–rejector names.