# 108+ Alternating Current (AC) GATE, Quiz, MCQs With Explanations

Alternating current (AC) is a type of electrical current that changes direction periodically. It is widely used in electrical power systems, electronic devices, and many other applications. Here are some multiple-choice questions (MCQs) about AC, along with explanations:

## What is the frequency of AC power used in most countries?

A) 50 Hz
B) 60 Hz
C) 100 Hz
D) 120 Hz
Answer: A) 50 Hz. Most countries in the world use AC power with a frequency of 50 Hz, while some countries, including the United States, use a frequency of 60 Hz.

## What is the peak voltage of an AC signal with a root mean square (RMS) voltage of 120 V?

A) 170 V
B) 240 V
C) 340 V
D) 480 V
Answer: B) 240 V. The peak voltage of an AC signal is equal to the RMS voltage multiplied by the square root of 2, which is approximately 1.414. Therefore, the peak voltage of an AC signal with an RMS voltage of 120 V is approximately 170 V x 1.414 = 240 V.

## What is the phase difference between two AC signals that have a frequency of 60 Hz and a time difference of 1/120 seconds?

A) 15 degrees
B) 30 degrees
C) 45 degrees
D) 60 degrees
Answer: C) 45 degrees. The phase difference between two AC signals is given by the formula 360 x (time difference) x (frequency). In this case, the time difference is 1/120 seconds, and the frequency is 60 Hz, so the phase difference is 360 x (1/120) x (60) = 45 degrees.

## What is the reactance of a 100 mH inductor at a frequency of 50 Hz?

A) 0.1 ohms
B) 10 ohms
C) 31.4 ohms
D) 314 ohms
Answer: C) 31.4 ohms. The reactance of an inductor is given by the formula 2 x pi x frequency x inductance. In this case, the frequency is 50 Hz, and the inductance is 100 mH (0.1 H), so the reactance is 2 x 3.14 x 50 x 0.1 = 31.4 ohms.

## What is the power factor of a circuit that has a resistance of 50 ohms and a reactance of 30 ohms at a frequency of 60 Hz?

A) 0.5
B) 0.6
C) 0.8
D) 1.0
Answer: B) 0.6. The power factor of a circuit is given by the formula cos(theta), where theta is the phase angle between the voltage and current. In this case, the resistance is 50 ohms and the reactance is 30 ohms, so the phase angle is arctan(30/50) = 33.7 degrees. Therefore, the power factor is cos(33.7) = 0.6.

## What is the impedance of a circuit that has a resistance of 50 ohms and a reactance of 30 ohms?

A) 10 ohms
B) 40 ohms
C) 58.3 ohms
D) 70.7 ohms
Answer: C) 58.3 ohms. The impedance of a circuit is given by the formula Z = sqrt(R^2 + X^2), where R is the resistance and X is the reactance. In this case, R = 50 ohms and X = 30 ohms, so Z = sqrt(50^2 + 30^2) = 58.3 ohms.

## What is the average power dissipated by a 100-ohm resistor in an AC circuit with a voltage amplitude of 120 V and a frequency of 50 Hz?

A) 28.8 W
B) 57.7 W
C) 115.5 W
D) 231 W
Answer: A) 28.8 W. The average power dissipated by a resistor in an AC circuit is given by the formula P = Vrms^2/R, where Vrms is the RMS voltage and R is the resistance. In this case, the voltage amplitude is 120 V, so the RMS voltage is 120/sqrt(2) = 84.8 V. Therefore, the power dissipated by the resistor is (84.8^2)/100 = 28.8 W.

## What is the phase angle between the voltage and current in a purely capacitive AC circuit?

A) 0 degrees
B) 45 degrees
C) 90 degrees
D) 180 degrees
Answer: C) 90 degrees. In a purely capacitive AC circuit, the voltage and current are 90 degrees out of phase with each other. This is because the current leads the voltage in a capacitor, as the capacitor charges and discharges in response to the voltage.

## What is the reactance of a 10 uF capacitor at a frequency of 1 kHz?

A) 0.16 ohms
B) 1.59 ohms
C) 15.9 ohms
D) 159 ohms
Answer: B) 1.59 ohms. The reactance of a capacitor is given by the formula 1/(2 x pi x frequency x capacitance). In this case, the frequency is 1 kHz and the capacitance is 10 uF (0.00001 F), so the reactance is 1/(2 x 3.14 x 1000 x 0.00001) = 1.59 ohms.

## What is the power factor of a circuit that has a purely inductive load with a reactance of 50 ohms at a frequency of 60 Hz?

A) 0.5
B) 0.707
C) 0.866
D) 1.0
Answer: A) 0.5. In a purely inductive AC circuit, the current lags the voltage by 90 degrees, which gives a power factor of cos(90) = 0. Therefore, the power factor of a circuit with a purely inductive load is always less than 1 and can be as low as 0.

## Which of the following is a characteristic of an ideal inductor?

a) Zero inductance
b) Infinite inductance
c) Zero resistance
d) Infinite resistance
Explanation: An ideal inductor is a hypothetical component that has infinite inductance, zero resistance, and can store energy indefinitely. In practice, all inductors have some resistance and a finite inductance value.

## Which of the following is not a type of transformer?

a) Step-up transformer
b) Step-down transformer
c) Isolation transformer
d) Transistor transformer
Explanation: There is no such thing as a “transistor transformer”. The three main types of transformers are step-up transformers, step-down transformers, and isolation transformers.

## A sinusoidal voltage source has an RMS voltage of 120 V. What is the peak voltage of the source?

a) 170 V
b) 240 V
c) 60 V
d) 85 V
Explanation: The peak voltage of a sinusoidal waveform is equal to the RMS voltage multiplied by the square root of 2. Therefore, the peak voltage of a sinusoidal voltage source with an RMS voltage of 120 V is 120 x √2 = 169.7 V. However, since this is a multiple-choice question, we need to choose the closest option, which is 240 V.

## Which of the following is true about capacitors in AC circuits?

a) Capacitors block DC current and allow AC current to pass through.
b) Capacitors block AC current and allow DC current to pass through.
c) Capacitors block both DC and AC currents.
d) Capacitors allow both DC and AC currents to pass through.
Answer: a) Capacitors block DC current and allow AC current to pass through.
Explanation: Capacitors act as open circuits to DC current, but as the frequency of the applied voltage increases, the capacitor’s impedance decreases and it starts to allow current to flow through it. Therefore, in AC circuits, capacitors block DC current and allow AC current to pass through.

## Which of the following is a unit of inductance?

a) Ohm
c) Henry
d) Volt
Explanation: The unit of inductance is the Henry, named after the American scientist Joseph Henry. One Henry is defined as the amount of inductance that induces an electromotive force of one volt when the current through it changes at a rate of one ampere per second.

## A coil has a resistance of 10 ohms and an inductance of 2 H. What is the impedance of the coil at a frequency of 50 Hz?

a) 10 ohms
b) 20 ohms
c) 30 ohms
d) 40 ohms
Explanation: The impedance of a coil is given by the formula Z = √(R^2 + X^2), where R is the resistance and X is the reactance. For an inductor, the reactance is given by X = 2πfL, where f is the frequency and L is the inductance. Substituting the given values, we get X = 2π x 50 x 2 = 628 ohms. Therefore, Z = √(10^2 + 628^2) = 40 ohms.

## Which of the following is not a characteristic of an ideal transformer?

a) Zero leakage inductance
b) Infinite coupling coefficient
c) Zero core losses
d) Infinite impedance
Explanation: An ideal transformer is a hypothetical component that has perfect coupling, zero leakage inductance, zero core losses, and can transfer power without any losses. However, an ideal transformer still has a finite impedance, just like any real transformer.

## A 1 uF capacitor is connected in series with a 2 k ohm resistor across a 50 Hz AC voltage source. What is the capacitive reactance of the capacitor?

a) 0.032 ohms
b) 31.8 ohms
c) 318 ohms
d) 320 ohms
Explanation: The capacitive reactance of a capacitor is given by Xc = 1/(2πfC), where f is the frequency and C is the capacitance. Substituting the given values, we get Xc = 1/(2π x 50 x 1E-6) = 31.8 ohms.

## What is the power factor of a purely resistive load?

a) 0
b) 0.5
c) 1
d) undefined
Explanation: A purely resistive load has no reactance, and therefore the voltage and current waveforms are in phase with each other. This means that the power factor, which is the cosine of the angle between the voltage and current waveforms, is equal to 1.

## A 50 Hz AC voltage source has a peak voltage of 200 V. What is the rms voltage of the source?

a) 100 V
b) 141 V
c) 200 V
d) 282 V
Explanation: The rms voltage of a sinusoidal waveform is equal to the peak voltage divided by the square root of 2. Therefore, the rms voltage of a 50 Hz AC voltage source with a peak voltage of 200 V is 200 / √2 = 141.4 V.

## What is the reactance of a 50 µF capacitor at 100 Hz?

A. 3.18 kΩ
B. 31.8 kΩ
C. 318 kΩ
D. 3.18 Ω

Explanation: The reactance of a capacitor is given by the formula Xc = 1/(2πfC), where Xc is the capacitive reactance, f is the frequency and C is the capacitance. Substituting the given values, we get:

Xc = 1/(2π10050*10^-6)
= 3.18 kΩ

Therefore, option A is the correct answer.

## A resistor of 100 Ω and an inductor of 1.0 H are connected in series to a 60 Hz AC source. What is the total impedance of the circuit?

A. 100 Ω
B. 116 Ω
C. 166 Ω
D. 60 Ω

Explanation: The impedance of a series RL circuit is given by the formula Z = √(R^2 + Xl^2), where R is the resistance, Xl is the inductive reactance, and Z is the impedance.

Xl = 2πfL = 2π601 = 377 Ω (inductive reactance)

Z = √(R^2 + Xl^2) = √(100^2 + 377^2) = 116 Ω

Therefore, option B is the correct answer.

## In a series RC circuit, the voltage across the capacitor leads the current by:

A. 0°
B. 90°
C. 180°
D. 45°

Explanation: In a series RC circuit, the voltage across the capacitor leads the current by 90°. This is because the current through a capacitor is proportional to the rate of change of voltage across it. Since the voltage across a capacitor in a series RC circuit varies sinusoidally, the current through the capacitor is also sinusoidal but phase-shifted by 90°.

Therefore, option B is the correct answer.

## A series RLC circuit resonates at a frequency of 10 kHz. If the capacitance is increased by a factor of 4 and the inductance is decreased by a factor of 4, what will be the resonant frequency of the circuit?

A. 2.5 kHz
B. 5 kHz
C. 10 kHz
D. 20 kHz

Explanation: The resonant frequency of a series RLC circuit is given by the formula:

fr = 1/(2π√(LC))

If the capacitance is increased by a factor of 4, the new capacitance C’ = 4C. If the inductance is decreased by a factor of 4, the new inductance L’ = L/4.

Substituting the new values in the formula for resonant frequency, we get:

fr’ = 1/(2π√(C’L’))
= 1/(2π√(4CL/4))
= 1/(2π√(CL))
= fr

Therefore, the resonant frequency of the circuit remains unchanged and is still 10 kHz. Option C is the correct answer.

## In an AC circuit, the current lags behind the voltage by 90 degrees in a:

a) Capacitive circuit
b) Resistive circuit
c) Inductive circuit
d) None of the above

a) Zero
b) Negative
c) Positive
d) Unity

a) 90 degrees
b) 180 degrees
c) 0 degrees
d) 45 degrees

a) 31.8 ohms
b) 318 ohms
c) 5 ohms
d) 50 ohms

## In a circuit containing resistance, inductance, and capacitance, the phase angle between the voltage and current is:

a) Always zero
b) Always 90 degrees
c) Less than 90 degrees
d) Greater than 90 degrees
Answer: c) Less than 90 degrees

Explanation: The phase angle between the voltage and current in a circuit containing resistance, inductance, and capacitance can vary and is typically less than 90 degrees.

## Which of the following parameters remains constant in an AC circuit having only resistance?

a) Voltage
b) Current
c) Power
d) None of the above

a) Hertz (Hz)
b) Volts (V)
c) Amperes (A)
d) Ohms (Ω)

a) 0 degrees
b) 90 degrees
c) 180 degrees
d) 270 degrees

a) Frequency
b) Inductance
c) Resistance
d) Current

## The power factor of an AC circuit having only a capacitive load is:

a) Zero
b) Negative
c) Positive
d) Unity

Explanation: The power factor of an AC circuit having only a capacitive load is zero because the current leads the voltage by 90 degrees, resulting in zero power being delivered to the load.

## What is the phase relationship between the voltage and current in a purely resistive AC circuit?

a) Voltage leads current by 90 degrees
b) Current leads voltage by 90 degrees
c) Voltage and current are in phase
d) Voltage and current are out of phase
Answer: c) Voltage and current are in phase

a) Ohm (Ω)
b) Henry (H)
d) Siemens (S)

## The RMS value of an AC voltage is:

a) The average value of the voltage over one cycle
b) The maximum value of the voltage
c) The value of the voltage that produces the same heating effect as the DC voltage of the same value
d) The instantaneous value of the voltage at a particular point in time
Answer: c) The value of the voltage that produces the same heating effect as the DC voltage of the same value

a) Oscilloscope
b) Voltmeter
c) Multimeter
d) Wattmeter

## Which of the following is a disadvantage of using AC power transmission over long distances?

a) High voltage can be easily produced
b) AC generators are more efficient than DC generators
c) AC power is easier to transform than DC power
d) AC power transmission suffers from power loss due to the skin effect
Answer: d) AC power transmission suffers from power loss due to the skin effect

Explanation: The skin effect causes the current to flow mostly on the surface of the conductor, resulting in increased resistance and power loss in AC power transmission over long distances.