AC Circuits Study Materials for Competitive Exams

AC Circuits

Q. What is the formula for calculating the total current in a parallel RLC circuit? (2023)

A. I = V/R
B. I = V/(1/R + 1/X)
C. I = V/(R + X)
D. I = V/R + V/X

Solution

In a parallel RLC circuit, the total current is calculated using I = V/(1/R + 1/X), where X is the total reactance.

Correct Answer: B — I = V/(1/R + 1/X)

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Q. What is the formula for the average power consumed in an AC circuit with a phase angle φ? (2020)

A. P = VI
B. P = VI cos(φ)
C. P = VI sin(φ)
D. P = V²/R

Solution

The average power P in an AC circuit is given by P = VI cos(φ), where φ is the phase angle.

Correct Answer: B — P = VI cos(φ)

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Q. What is the formula for the average power consumed in an AC circuit with a resistor? (2019)

A. P = VI
B. P = V²/R
C. P = I²R
D. All of the above

Solution

The average power consumed in an AC circuit can be expressed as P = VI, P = V²/R, and P = I²R.

Correct Answer: D — All of the above

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Q. What is the formula for the resonant frequency of an RLC circuit? (2021)

A. f = 1/(2π√(LC))
B. f = R/(2πL)
C. f = 1/(2πRC)
D. f = 2π√(LC)

Solution

The resonant frequency f of an RLC circuit is given by f = 1/(2π√(LC)).

Correct Answer: A — f = 1/(2π√(LC))

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Q. What is the formula for the total impedance in a parallel RLC circuit? (2023)

A. 1/Z = 1/Z1 + 1/Z2 + 1/Z3
B. Z = R + jX
C. Z = R
D.
. X
. Z = R + jωL - j/(ωC)

Solution

The total impedance in a parallel circuit is given by 1/Z = 1/Z1 + 1/Z2 + 1/Z3.

Correct Answer: A — 1/Z = 1/Z1 + 1/Z2 + 1/Z3

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Q. What is the formula for the total impedance in a series RLC circuit? (2023)

A. Z = R + j(XL - XC)
B. Z = R + jXL + jXC
C. Z = R + jωL
D. Z = R + jωC

Solution

The total impedance in a series RLC circuit is given by Z = R + j(XL - XC).

Correct Answer: A — Z = R + j(XL - XC)

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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 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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AC Circuits

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