Unit – 9 Electrical circuits and Electronics | R-L and R-C circuits

AC Circuits with R–L and R–C – TRB Competitive Exam Notes

In alternating current (AC) circuits, resistance (R), inductance (L), and capacitance (C) affect the current and voltage differently. For TRB, BRTE, and other competitive exams, questions are frequently asked from R–L and R–C circuits focusing on impedance, phase difference, power factor, and resonance concepts.

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1. R–L Circuit (Resistance–Inductance Circuit)

An R–L circuit consists of a resistor and an inductor connected in series with an AC source.

Impedance of R–L Circuit

The opposition offered to AC is called impedance (Z).

Inductive reactance:

X_L = 2πfL

Total impedance:

Z = √(R² + X_L²)

Phase Angle

In an R–L circuit, current lags voltage.

tan φ = X_L / R

Power Factor

cos φ = R / Z    (Lagging)

Important Points (TRB Focus)

• Current lags voltage
• Power factor is lagging
• Energy is stored in the magnetic field

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2. R–C Circuit (Resistance–Capacitance Circuit)

An R–C circuit consists of a resistor and a capacitor connected in series with an AC source.

Impedance of R–C Circuit

Capacitive reactance:

X_C = 1 / (2πfC)

Total impedance:

Z = √(R² + X_C²)

Phase Angle

In an R–C circuit, current leads voltage.

tan φ = X_C / R

Power Factor

cos φ = R / Z    (Leading)

Important Points (TRB Focus)

• Current leads voltage
• Power factor is leading
• Energy is stored in the electric field

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3. Shortcut Tricks for TRB Exams

• L → Lagging (Inductor → Current lags)
• C → Current Comes first (Current leads in capacitor)
• If frequency increases:
  • X_L increases
  • X_C decreases
• Pure R → Phase angle = 0°
• Pure L → Phase angle = 90° lag
• Pure C → Phase angle = 90° lead

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4. Comparison Table: R–L vs R–C Circuit

Feature	R–L Circuit	R–C Circuit
Reactance	XL = 2πfL	XC = 1 / (2πfC)
Impedance	√(R2 + XL2)	√(R2 + XC2)
Phase Relation	Current lags voltage	Current leads voltage
Power Factor	Lagging	Leading
Energy Stored In	Magnetic field	Electric field

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5. TRB Level MCQs (10 Questions)

1. In an R–L circuit, the current:
   (A) Leads voltage
   (B) Lags voltage
   (C) In phase
   (D) Zero
   Answer: (B)
2. Inductive reactance depends on:
   (A) Resistance
   (B) Frequency
   (C) Voltage
   (D) Power
   Answer: (B)
3. Unit of inductive reactance is:
   (A) Henry
   (B) Ohm
   (C) Farad
   (D) Tesla
   Answer: (B)
4. In an R–C circuit, power factor is:
   (A) Unity
   (B) Zero
   (C) Leading
   (D) Lagging
   Answer: (C)
5. Capacitive reactance decreases when:
   (A) Frequency decreases
   (B) Frequency increases
   (C) Resistance increases
   (D) Voltage increases
   Answer: (B)
6. The phase angle in pure inductive circuit is:
   (A) 0°
   (B) 45°
   (C) 90°
   (D) 180°
   Answer: (C)
7. Power consumed in pure inductive circuit is:
   (A) Maximum
   (B) Minimum
   (C) Zero
   (D) Infinite
   Answer: (C)
8. Impedance is minimum when:
   (A) R = 0
   (B) L = 0
   (C) C = 0
   (D) XL = XC
   Answer: (D)
9. Energy in capacitor is stored in:
   (A) Magnetic field
   (B) Electric field
   (C) Thermal field
   (D) Gravitational field
   Answer: (B)
10. Which circuit has leading current?
    (A) R–L
    (B) R–C
    (C) Pure R
    (D) R–L–C
    Answer: (B)

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Exam Tip: Questions from AC circuits are often direct and formula-based in TRB. Focus on phase relation, power factor, and frequency dependence.