Power Factor Questions

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Very Short Answers Questions [1 Mark Questions]

Ques. What will happen to the overall power for a power system having induction motor loads and a synchronous motor, which is overexcited, is also attached to it?

1. Overall power factor degrades
2. Overall power factor improves
3. Overall power factor becomes up
4. Overall power factor remains the same

Ans. The correct answer is b. Overall power factor improves

Explanation: When the synchronous motor becomes overexcited and performed as a source of lagging reactive power, hence the overall power factor improves.

Ques. In an AC circuit, how many types of power can be defined?

1. 5
2. 1
3. 3
4. 2

Ans. The correct answer is c. 3

Explanation: In an ac circuit three types of power can be defined i.e. average power, instantaneous power, and apparent power.

Ques. Which among the following is the power factor in a pure capacitive or inductive circuit?

1. Infinity
2. -1
3. Zero
4. 1

Ans. The correct answer is c. Zero

Explanation: In a pure capacitive or inductive circuit, the phase angle (ϕ) between the voltage and the current is π/2.

The power factor is given by cos ϕ. Therefore the power factor for a pure capacitive or inductive circuit is cos π/2 i.e. equals zero.

Ques. In the case of ____ circuits, the power factor is called the leading power factor.

1. LC
2. LR
3. RLC
4. RC

Ans. The correct answer is d. RC

Explanation: The power factor In the case of RC circuits, is known as the leading power factor.

Ques. Which among the following is the power factor in a pure resistive circuit?

1. Zero
2. 1
3. -1
4. Infinity

Ans. The correct answer is b. 1

Explanation: In a pure resistive circuit, the phase angle (ϕ) between the voltage and the current is 0.

The power factor is given by cos ϕ. Therefore the power factor for a pure resistive circuit is cos 0 i.e. equals one.

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Short Answers Questions [2 Marks Questions]

Ques. What is the power factor?

Ans. The power factor is a measure of how efficiently a device operates with the power it receives. It is represented by the cosine of the phase angle between the voltage and the current in an ac circuit i.e.

Power factor = cos ϕ

Ques. What is the formula and unit of power factor?

Ans. The formula of power factor is given by

Power factor = True power / Apparent power = True power / rms power

Since the power factor is the ratio of true power to the apparent power, therefore, it is a unitless quantity.

Ques. Explain the concept of lagging and leading power factors.

Ans. A situation where the current lags behind the voltage in an ac circuit due to the presence of inductive loads refers to as the lagging power factor.

A situation where the current leads the voltage in an ac circuit due to the presence of capacitive loads refers to as the leading power factor.

Ques. A supply system supplies the load 800 kW at a power factor of 0.8 leading. Calculate the reactive power.

Ans. Given

• True power (P) = 800 kW
• Power factor (PF) = 0.8

Therefore, Apparent power (S) = True power / power factor

⇒ S = 800 / 0.8 = 1000 W

We have

Reactive power (Q) = Apparent power (S) x √(1 - PF²)

Reactive power (Q) = 1000 x √(1 - 0.8²)

Reactive power (Q) = 600 W

Also Read:

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Long Answers Questions [3 Marks Questions]

Ques. What are the causes of the low power factor?

Ans. The following are the causes of the low power factor of an ac circuit

• The main cause of the low power factor is inductive loads such as electric motors, transformers, etc.
• The existence of harmonic current in the system.
• The uneven distribution of loads in the electrical system results in an unbalanced power factor.
• Transformers operating close to their rated capacity can show lower power factor characteristics.

Ques. A load is connected to an ac source. The true power dissipated in the load of the ac circuit is 500 W and the apparent power supplied by the source is 1000 VA. What is the power factor of the circuit?

Ans. Given

• The true power dissipated in the load, P = 500 W
• The apparent power supplied by the source, S = 1000 VA = 1000 W

The power factor of the circuit is given by

Power factor, cos ϕ = P/S

⇒ Power factor, cos ϕ = 500/1000 = 0.5

Ques. An inductor of 100 mH, a capacitor of 400 µF, and a resistor of 20 Ω are connected in series with a 15 V, variable frequency ac source. Calculate the frequency at which the power factor of the circuit is unity.

Ans. Given

• The inductance of the inductor, L = 100 mH
• The capacitance of the capacitor, C = 400 µF
• The resistance of the resistor, R = 15 Ω

Given that the power factor (cos ϕ) of the circuit is unity it represents a purely resistive circuit. Also, in a purely resistive circuit, inductive reactance is equal to capacitive reactance i.e.

ω₀L = 1/Cω₀

⇒ ω₀ = 1/√(LC)

But ω₀ = 2πf₀

⇒ 2πf₀ = 1/√(LC)

⇒ f₀ = 1/2π√(LC)

⇒ f₀ = 1/2π√(100 x 10^-3 x 400 x 10^-6)

⇒ f₀ = 0.025 x 10^-3 Hz

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Very Long Answers Questions [5 Marks Questions]

Ques. A sinusoidal voltage V = 200 sin 314 t is applied to a resistor of 10 Ω resistance. Calculate

1. The rms value of the voltage
2. The rms value of current
3. The power dissipated as heat in watt

Ans. The given equation of voltage is

V = 200 sin 314 t 

Comparing it with the equation of alternating voltage

V = V₀ sinωt

We get

• The peak value of the voltage or maximum voltage, V₀ = 200 V
• Angular frequency, ω = 314 rad/s

Also given the resistance of the resistor, R = 10 Ω

1. The rms value of the voltage is given by

V_rms = V₀/√2 = 200/√2 = 141.4 V

2. The rms value of the current is given by

I_rms = V_rms/R = 141.4/10 = 14.14 A

100. Since the circuit is purely resistive, therefore power factor (cos ϕ) of the circuit is one.

The power dissipated as heat is given by

P = V_rms I_rms cos ϕ

⇒ P = 141.4 x 14.14 x 1 = 1999.4 W ≅ 2 kW

Ques. An inductor of unknown value, a capacitor of 100 µF, and a resistor of 10 Ω are connected in series to a 220 V, 50 Hz ac source. It is found that the power factor of the circuit is unity. Calculate the inductance of the inductor and the current amplitude.

Ans. Given

• The capacitance of the capacitor, C = 100 µF
• The resistance of the resistor, R = 10 Ω
• Applied voltage, V = 220 V
• The frequency of the supply voltage, f = 50 Hz

Given that the power factor (cos ϕ) of the circuit is unity it represents a purely resistive circuit.

Hence the total impedance (Z) of the circuit is equal to the resistance of the resistor (R) i.e Z = R

The rms value of current, Irms = V_rms/Z = V_rms/R

⇒ I_rms = 220/10 = 22 A

Therefore the current amplitude, I₀ = √2I_rms = √2 x 22 = 31.1 A

Now in a purely resistive circuit, inductive reactance is equal to capacitive reactance i.e.

ω₀L = 1/Cω₀

⇒ ω₀ = 1/√(LC)

But ω₀ = 2πf₀

⇒ 2πf₀ = 1/√(LC)

⇒ f₀= 1/2π√(LC)

⇒ L = 1/4π²f₀² C

⇒ L = 1/ (4 x 3.14² x 50² x 100 x 10^-6) = 0.1 H

Ques. An inductor of 200 mH, a capacitor of 500 µF, and a resistor of 10 Ω are connected in series with 10 V, variable frequency ac source. Calculate

1. The frequency at which the power factor of the circuit is unity
2. The current amplitude at this frequency

Ans. Given

• The inductance of the inductor, L = 200 mH
• The capacitance of the capacitor, C = 500 µF
• The resistance of the resistor, R = 10 Ω

Given that the power factor (cos ϕ) of the circuit is unity it represents a purely resistive circuit.

1. Now in a purely resistive circuit, inductive reactance is equal to capacitive reactance i.e.

ω₀L = 1/Cω₀

⇒ ω₀ = 1/√(LC)

But ω₀ = 2πf₀

⇒ 2πf₀ = 1/√(LC)

⇒ f₀ = 1/2π√(LC)

⇒ f₀ = 1/2π√(200 x 10^-3 x 500 x 10^-6)

⇒ f₀ = 16 Hz

2. f₀ represents here a resonance frequency, and at resonant frequency current is maximum.

We know, I_rms = V_rms/Z = V_rms/R = 100/10 = 10 A

Therefore, the current amplitude is given by

I₀ = √2I_rms = √2 x 10 = 14.14 A

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