AC Circuits Study Materials for Competitive Exams

AC Circuits

Q. What is the impedance of a circuit with a resistance of 4 ohms and a reactance of 3 ohms? (2021)

A. 5 ohms
B. 7 ohms
C. 1 ohm
D. 12 ohms

Solution

Impedance Z = √(R² + X²) = √(4² + 3²) = √(16 + 9) = √25 = 5 ohms.

Correct Answer: A — 5 ohms

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Q. What is the impedance of a circuit with a resistance of 4Ω and a reactance of 3Ω? (2020)

A. 5Ω
B. 7Ω
C. 1Ω
D. 12Ω

Solution

Impedance Z = √(R² + X²) = √(4² + 3²) = √(16 + 9) = √25 = 5Ω.

Correct Answer: A — 5Ω

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Q. What is the impedance of a circuit with a resistor of 10Ω and an inductor of 0.1 H at a frequency of 50 Hz? (2022)

A. 10Ω
B. 15.71Ω
C. 20Ω
D. 5Ω

Solution

Impedance Z = √(R² + (XL)²), where XL = 2πfL = 31.42Ω. Thus, Z = √(10² + 31.42²) = 15.71Ω.

Correct Answer: B — 15.71Ω

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Q. What is the impedance of a circuit with a resistor of 10Ω and an inductor of 0.1H at a frequency of 50Hz? (2022)

A. 10Ω
B. 15.71Ω
C. 20Ω
D. 25Ω

Solution

Impedance Z = √(R² + (XL)²), where XL = 2πfL = 31.42Ω. Thus, Z = √(10² + 31.42²) = 15.71Ω.

Correct Answer: B — 15.71Ω

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Q. What is the impedance of a circuit with a resistor of 4Ω and a capacitor of 2μF at a frequency of 50Hz? (2020)

A. 4Ω
B. 5Ω
C. 6Ω
D. 8Ω

Solution

Impedance Z = √(R² + (1/(ωC))²) where ω = 2πf. Here, R = 4Ω, C = 2μF, f = 50Hz. Calculate Z.

Correct Answer: C — 6Ω

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Q. What is the impedance of a circuit with a resistor of 4Ω and an inductor of 3Ω at resonance? (2022)

A. 1Ω
B. 3Ω
C. 4Ω
D. 7Ω

Solution

At resonance, the impedance is equal to the resistance, which is 4Ω.

Correct Answer: C — 4Ω

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Q. What is the impedance of a series circuit containing a resistor (R) and an inductor (L) at angular frequency ω? (2020)

A. R
B. √(R² + (ωL)²)
C. R + jωL
D. R + L

Solution

The impedance Z in a series R-L circuit is given by Z = √(R² + (ωL)²).

Correct Answer: B — √(R² + (ωL)²)

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Q. What is the impedance of a series circuit containing a resistor (R) and an inductor (L) at a frequency (f)? (2020)

A. R
B. √(R² + (2πfL)²)
C. R + 2πfL
D. R - 2πfL

Solution

The impedance Z in a series RL circuit is given by Z = √(R² + (2πfL)²).

Correct Answer: B — √(R² + (2πfL)²)

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Q. What is the impedance of a series circuit with a resistor of 4Ω and an inductor of 3Ω at resonance? (2020)

A. 1Ω
B. 3Ω
C. 4Ω
D. 7Ω

Solution

At resonance, the impedance is equal to the resistance, which is 4Ω.

Correct Answer: C — 4Ω

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Q. What is the phase angle in a circuit with a resistance of 30 ohms and a reactance of 40 ohms? (2021)

A. 53.13°
B. 36.87°
C. 45°
D. 60°

Solution

θ = tan⁻¹(X/R) = tan⁻¹(40/30) = 53.13°.

Correct Answer: A — 53.13°

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Q. What is the phase difference between the voltage and current in a purely resistive AC circuit? (2021)

A. 0°
B. 45°
C. 90°
D. 180°

Solution

In a purely resistive circuit, the voltage and current are in phase, so the phase difference is 0°.

Correct Answer: A — 0°

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Q. What is the phase difference between the voltage and current in a series RLC circuit at resonance? (2023)

A. 0°
B. 90°
C. 180°
D. 45°

Solution

At resonance in a series RLC circuit, the phase difference between voltage and current is 0°.

Correct Answer: A — 0°

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Q. What is the power consumed in an AC circuit with a voltage of 230V and a current of 5A with a power factor of 0.8? (2023)

A. 920W
B. 1150W
C. 115W
D. 460W

Solution

Power = V × I × Power Factor = 230V × 5A × 0.8 = 920W.

Correct Answer: A — 920W

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Q. What is the power factor in a circuit with a resistance of 5 ohms and a reactance of 5 ohms? (2022)

A. 0
B. 0.5
C. 1
D. √2/2

Solution

Power factor = R/Z = 5/√(5² + 5²) = 5/√50 = √2/2.

Correct Answer: D — √2/2

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Q. What is the power factor in an AC circuit with a phase angle of 30 degrees? (2022)

A. 0.5
B. 0.866
C. 1
D. 0.707

Solution

The power factor is cos(30°) = √3/2 ≈ 0.866.

Correct Answer: B — 0.866

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Q. What is the power factor of a circuit with a resistance of 30Ω and a reactance of 40Ω? (2023)

A. 0.6
B. 0.75
C. 0.8
D. 1.0

Solution

Power factor = R/Z where Z = √(R² + X²). Calculate.

Correct Answer: A — 0.6

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Q. What is the power factor of a circuit with a resistance of 4Ω and a reactance of 3Ω? (2021)

A. 0.6
B. 0.8
C. 1.0
D. 0.75

Solution

Power factor = R/Z = R/√(R² + X²) = 4/√(4² + 3²) = 4/5 = 0.8.

Correct Answer: A — 0.6

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Q. What is the power factor of a circuit with a resistance of 5 ohms and a reactance of 5 ohms? (2022)

A. 0
B. 0.5
C. 1
D. √2/2

Solution

Power factor = R/Z = 5/√(5² + 5²) = 5/√50 = √2/2.

Correct Answer: D — √2/2

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Q. What is the power factor of a circuit with a resistance of 5Ω and an inductive reactance of 5Ω? (2022)

A. 0.5
B. 0.707
C. 1
D. 0

Solution

Power factor = R/Z = 5 / √(5² + 5²) = 5 / √50 = 0.707.

Correct Answer: B — 0.707

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Q. What is the power factor of a circuit with a resistance of 6Ω and a reactance of 8Ω? (2022)

A. 0.75
B. 0.8
C. 0.6
D. 1.0

Solution

Power factor = R/Z = R/√(R² + X²) = 6/√(6² + 8²) = 6/10 = 0.6.

Correct Answer: B — 0.8

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Q. What is the power factor of a circuit with a resistance of 8Ω and a reactance of 6Ω? (2023)

A. 0.5
B. 0.6
C. 0.8
D. 1.0

Solution

Power factor = R/Z, where Z = √(R² + X²) = √(8² + 6²) = 10. Thus, PF = 8/10 = 0.8.

Correct Answer: C — 0.8

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Q. What is the power factor of an AC circuit with a phase angle of 60°? (2022)

A. 0.5
B. 0.866
C. 1
D. 0.707

Solution

The power factor is cos(60°) = 0.5.

Correct Answer: B — 0.866

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Q. What is the total current in a circuit with a voltage of 240V, resistance of 20 ohms, and inductive reactance of 30 ohms? (2022)

A. 8 A
B. 6 A
C. 4 A
D. 10 A

Solution

Z = √(R² + Xl²) = √(20² + 30²) = √(400 + 900) = √1300 = 36.06 ohms. I = V/Z = 240/36.06 = 6.66 A.

Correct Answer: B — 6 A

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Q. What is the total current in a parallel circuit with two branches, one with 5A and the other with 3A? (2022)

A. 8A
B. 15A
C. 2.5A
D. 5A

Solution

Total current in parallel = I1 + I2 = 5A + 3A = 8A.

Correct Answer: A — 8A

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Q. What is the total current in a series circuit with a 10Ω resistor and a 20Ω inductor connected to a 100V AC source at 50Hz? (2023)

A. 2A
B. 4A
C. 5A
D. 10A

Solution

Total impedance Z = √(R² + (ωL)²) = √(10² + (2π(50)(20))²). Calculate to find current.

Correct Answer: B — 4A

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AC Circuits

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