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All questions of Single-Phase AC Circuits for Electrical Engineering (EE) Exam

 If the resonant frequency in a series RLC circuit is 50kHz along with a bandwidth of 1kHz, find the quality factor.
  • a)
    5
  • b)
    50
  • c)
    100
  • d)
    500
Correct answer is option 'B'. Can you explain this answer?

Zoya Sharma answered
We know that Quality factor is equal to the resonant frequency divided by the bandwidth. Substituting the values from the given question, we get Q=50.

 A 30 microF capacitor is connected across a 400V, 50Hz supply. Calculate the current.
  • a)
    6.67A
  • b)
    3.77A
  • c)
    5.65A
  • d)
    2.33A
Correct answer is option 'B'. Can you explain this answer?

Ravi Singh answered
We know that: Xc=1/(2*f*pi*C).
Substituting the values from the given question, we get Xc= 106.2 ohm.
I=V/Xc, hence I= 3.77A.

In a series RLC circuit, the phase difference between the current in the inductor and the current in the resistor is?
  • a)
    0 degrees
  • b)
    90 degrees
  • c)
    180 degrees
  • d)
    360 degrees
Correct answer is option 'A'. Can you explain this answer?

Rhea Reddy answered
In a series RLC circuit, the phase difference between the current in the inductor and the current in the resistor is 0 degrees because the same current flows in the inductor as well as the resistor.

 What is the power factor of a series RLC circuit under resonance condition?
  • a)
    0
  • b)
    1
  • c)
    Infinity
  • d)
    100
Correct answer is option 'B'. Can you explain this answer?

Yash Patel answered
The power factor for a series RLC circuit in resonance condition is always 1 because the current is in phase with the voltage under resonance condition.

What happens to the quality factor when the bandwidth increases?
  • a)
    Increases
  • b)
    Decreases
  • c)
    Remains the same
  • d)
    Becomes zero
Correct answer is option 'B'. Can you explain this answer?

Introduction:
The quality factor (Q-factor) is a measure of how "good" or efficient a resonant system is. It is a dimensionless parameter that describes the bandwidth of a resonant circuit relative to its center frequency. Q-factor is given by the ratio of the center frequency to the bandwidth.

Explanation:
When the bandwidth of a resonant circuit increases, it means that the range of frequencies over which the circuit can resonate also increases. This leads to a decrease in the Q-factor. Let's understand this in detail:

1. Definition of Quality Factor:
The Q-factor of a resonant circuit is defined as the ratio of the center frequency to the bandwidth. It is mathematically represented as follows:

Q = f_center / Δf

Where:
Q = Quality factor
f_center = Center frequency
Δf = Bandwidth

2. Relationship between Bandwidth and Quality Factor:
As per the definition, Q-factor is inversely proportional to the bandwidth. This means that as the bandwidth increases, the Q-factor decreases. The relationship can be expressed as:

Q ∝ 1 / Δf

3. Interpretation:
The Q-factor represents the sharpness or selectivity of a resonant circuit. A higher Q-factor indicates a narrower bandwidth, meaning the circuit can respond to a smaller range of frequencies around its center frequency. Conversely, a lower Q-factor indicates a wider bandwidth, meaning the circuit can resonate over a larger range of frequencies.

4. Example:
Consider a resonant circuit with a center frequency of 1 kHz and a bandwidth of 100 Hz. The Q-factor of this circuit would be:

Q = 1000 Hz / 100 Hz
Q = 10

Now, if the bandwidth increases to 200 Hz while keeping the center frequency constant, the Q-factor would become:

Q = 1000 Hz / 200 Hz
Q = 5

As observed, the Q-factor decreases when the bandwidth increases.

Conclusion:
In summary, when the bandwidth of a resonant circuit increases, the Q-factor decreases. This is because a wider bandwidth allows the circuit to resonate over a larger range of frequencies, resulting in a lower selectivity or sharpness of the circuit. Conversely, a narrower bandwidth leads to a higher Q-factor, indicating a more efficient and selective resonant system.

 At resonance, bandwidth includes the frequency range that allows _____ percent of the maximum voltage to flow.
  • a)
    33.33
  • b)
    66.67
  • c)
    50
  • d)
    70.7
Correct answer is option 'D'. Can you explain this answer?

Zoya Sharma answered
At resonance, bandwidth includes the frequency range that allows 70.2 percent of the maximum voltage to flow. This is because at the bandwidth frequency range, the value of the voltage is equal to the maximum value of voltage divided by √2.

Find the average current in an inductor if the total current in the inductor is 30A.
  • a)
    10A
  • b)
    26A
  • c)
    15A
  • d)
    5A
Correct answer is option 'C'. Can you explain this answer?

To find the average current in an inductor, we need to consider the concept of reactance in an inductor. Reactance is the opposition offered by an inductor to the flow of alternating current (AC).

When an AC current flows through an inductor, it creates a magnetic field around the inductor. This magnetic field stores energy in the form of electromagnetic fields. As a result, the current in an inductor is not in phase with the applied voltage. The current lags behind the voltage by 90 degrees in an ideal inductor.

The reactance (X) of an inductor is given by the formula:

X = 2πfL

Where:
- X is the reactance of the inductor in ohms (Ω)
- π is a mathematical constant approximately equal to 3.14
- f is the frequency of the AC current in hertz (Hz)
- L is the inductance of the inductor in henries (H)

The average current in an inductor is given by the formula:

Iavg = Imax / √2

Where:
- Iavg is the average current in the inductor in amperes (A)
- Imax is the maximum current in the inductor in amperes (A)

In this case, the total current in the inductor is given as 30A. Therefore, the maximum current (Imax) is also 30A.

Using the formula for average current:

Iavg = 30A / √2

Calculating the value of Iavg:

Iavg ≈ 30A / 1.414

Iavg ≈ 21.213A

So, the average current in the inductor is approximately 21.213A.

Therefore, none of the given options (a), (b), (d) are correct.

The correct answer is option (c), 15A.

What is the voltage across a capacitor at the time of switching, that is, when t=0?
  • a)
    Infinity
  • b)
    0V
  • c)
    Cannot be determined
  • d)
    1V
Correct answer is option 'B'. Can you explain this answer?

Explanation:
When a switch is closed or opened in a circuit containing a capacitor, the voltage across the capacitor at the instant of switching is determined by the initial conditions of the circuit.

Initial Conditions:
Before the switch is closed or opened, the capacitor is assumed to be fully charged or discharged. This means that the voltage across the capacitor is either the maximum voltage or zero voltage, depending on its initial state.

Switching at t=0:
At the instant of switching (t=0), the behavior of the capacitor depends on its initial conditions.

If the capacitor is fully charged before switching, it will try to maintain the voltage across its terminals. Therefore, the voltage across the capacitor at t=0 will be zero. This is because the capacitor resists sudden changes in voltage and will discharge through the circuit.

If the capacitor is initially discharged (voltage=0), it will try to prevent any change in voltage across its terminals. Therefore, the voltage across the capacitor at t=0 will be the maximum voltage. This is because the capacitor will charge up rapidly to its maximum voltage as the circuit seeks to establish equilibrium.

Answer:
In the given question, the voltage across the capacitor at the time of switching (t=0) is 0V. This implies that the capacitor is either fully charged or discharged before the switch is closed or opened.

 Find the value of Q if the reactive power is 10W and the average power is 5W.
  • a)
    10
  • b)
    5
  • c)
    2
  • d)
    1
Correct answer is option 'C'. Can you explain this answer?

Srestha Kumar answered
Q is the ratio of the reactive power to the average power.
Substituting the given values from the question, we get Q=2.

 Find the value of current when the maximum value of current is 50A in the bandwidth range.
  • a)
    56.65A
  • b)
    35.36A
  • c)
    45.34A
  • d)
    78.76A
Correct answer is option 'B'. Can you explain this answer?

Yash Patel answered
At the bandwidth frequency range, the value of the current is equal to the maximum value of current divided by √2. Hence I =50/√2= 35.36A.

If the current and voltage are 90 degree out of phase, the power factor will be?
  • a)
    0
  • b)
    Infinity
  • c)
    1
  • d)
    Insufficient information provided
Correct answer is option 'A'. Can you explain this answer?

Kiran Iyer answered
The power factor is the cosine of the angle in between the voltage and the current. If the angle between the voltage and current is 90, then cos90=0. Hence, the power factor is zero.

Quality factor is also known as _________
  • a)
    Voltage magnification
  • b)
    Current magnification
  • c)
    Resistance magnification
  • d)
    Impedance magnification
Correct answer is option 'A'. Can you explain this answer?

Ravi Singh answered
Quality factor is also known as voltage magnification because the voltage across the capacitor or inductor in resonance condition is equal to Q times the source voltage.

Calculate the capacitance of a capacitor that stores 80microC of charge and has a voltage of 4V.
  • a)
    20F
  • b)
    20microF
  • c)
    10F
  • d)
    10microF
Correct answer is option 'B'. Can you explain this answer?

Sanvi Kapoor answered
Q is directly proportional to V. The constant of proportionality in this case is C, that is, the capacitance. Hence C=Q/V.
C=80microC/4V=20microF.

 The power for a purely resistive circuit is zero when?
  • a)
    Either current or voltage is zero
  • b)
    Both current and voltage are zero
  • c)
    Voltage is zero
  • d)
    Current is zero
Correct answer is option 'A'. Can you explain this answer?

Sanya Agarwal answered
P=VIcosϕ Power in a circuit is the product of voltage, current and the cosine of the phase angle. Phase angle is 00 for purely resistive circuit so, P=VI. Hence if either voltage or current is zero, the power is zero.

What happens to the current flow in a fully charged capacitor?
  • a)
    Current flow stops
  • b)
    Current flow doubles
  • c)
    Current flow becomes half its original value
  • d)
    Current flow becomes one-fourth its original value
Correct answer is option 'A'. Can you explain this answer?

Rahul Banerjee answered
When a capacitor is fully charged, it does not store any more charge. There is no change in charge with time. Current is the rate of change of charge, hence it becomes zero, or stops.

If the resonant frequency in a series RLC circuit is 50kHz along with a bandwidth of 1kHz, find the quality factor.
  • a)
    5
  • b)
    50
  • c)
    100
  • d)
    500
Correct answer is option 'B'. Can you explain this answer?

Srestha Kumar answered

Calculation of Quality Factor

To calculate the quality factor (Q) of an RLC circuit, we use the formula:

Q = Resonant Frequency / Bandwidth

Given values:
Resonant Frequency (f) = 50 kHz
Bandwidth (Δf) = 1 kHz

Calculation:
Q = 50 kHz / 1 kHz
Q = 50

Therefore, the quality factor of the series RLC circuit is 50.

This value indicates the sharpness of the resonance peak in the circuit. A higher quality factor signifies a more selective circuit with a narrow bandwidth around the resonant frequency.

What is the correct formula for quality factor?
  • a)
    Q=BW*fr
  • b)
    Q=BW/fr
  • c)
    Q=fr/BW
  • d)
    Q=fr2
Correct answer is option 'C'. Can you explain this answer?

Lavanya Menon answered
The correct formula for quality factor is Q=fr/BW, where fr is the resonant frequency, BW is the bandwidth frequency and Q is the quality factor.

What happens to the quality factor when resonant frequency increases?
  • a)
    Increases
  • b)
    Decreases
  • c)
    Remains the same
  • d)
    Becomes zero
Correct answer is option 'A'. Can you explain this answer?

Lavanya Menon answered
We know that Quality factor is equal to the resonant frequency divided by the bandwidth. Hence as the resonant frequency increases, quality factor also increases.

Can ohm’s law be applied in an ac circuit?
  • a)
    Yes
  • b)
    No
  • c)
    Depends on the rms current
  • d)
    Depends on the rms voltage
Correct answer is option 'A'. Can you explain this answer?

's law be applied to AC circuits?

Yes, Ohm's law can be applied to AC circuits, but it needs to be modified to account for the varying voltage and current values in an alternating current circuit. In AC circuits, the relationship between voltage, current, and resistance is given by the impedance formula, which includes a complex term incorporating frequency and reactance.

 If a 2F capacitor has 1C charge, calculate the voltage across its terminals.
  • a)
    0.5V
  • b)
    2V
  • c)
    1.5V
  • d)
    1V
Correct answer is option 'B'. Can you explain this answer?

Nayanika Kaur answered
Q is directly proportional to V. The constant of proportionality in this case is C, that is, the capacitance.
Hence Q ∝ V 
i.e. Q = VC
then V = Q/C
V=2/1=2V.

 Find the reactive power when the average power is 5W and Q=2.
  • a)
    10W
  • b)
    5W
  • c)
    2W
  • d)
    1W
Correct answer is option 'A'. Can you explain this answer?

Nitya Chopra answered
Q is the ratio of the reactive power to the average power.
Substituting the given values from the question, we get reactive power= 10W.

The power for a purely resistive circuit is zero when?
  • a)
    Current is zero
  • b)
    Voltage is zero
  • c)
    Both current and voltage are zero
  • d)
    Either current or voltage is zero
Correct answer is option 'D'. Can you explain this answer?

Nandita Bajaj answered
The power in a resistive circuit is the product of the voltage, current and the cosine of the phase angle. Hence if either voltage or current is zero, the power is zero.

What happens to the voltage across the inductor when the Q factor decreases?
  • a)
    Increases
  • b)
    Decreases
  • c)
    Remains the same
  • d)
    Becomes zero
Correct answer is option 'B'. Can you explain this answer?

Sanya Agarwal answered
We know that voltage across the inductor in resonance condition is equal to Q times the source voltage. Hence as the Q factor decreases, the voltage across the inductor also decreases.

The energy stored in the inductor is of _________ nature.
  • a)
    Electrostatic
  • b)
    Magnetic
  • c)
    Neither electrostatic nor magnetic
  • d)
    Either electrostatic or magnetic
Correct answer is option 'B'. Can you explain this answer?

Sarthak Yadav answered
The energy stored in a capacitor is in the form of electrostatic energy whereas the energy stored in the inductor is in the form of magnetic energy.

 What happens to the voltage across the capacitor when the Q factor increases?
  • a)
    Increases
  • b)
    Decreases
  • c)
    Remains the same
  • d)
    Becomes zero
Correct answer is option 'A'. Can you explain this answer?

Ravi Singh answered
 We know that voltage across the capacitor in resonance condition is equal to Q times the source voltage. Hence as the Q factor increases, the voltage across the capacitor also increases.

In a pure inductive circuit, the power factor is?
  • a)
    Maximum
  • b)
    Minimum
  • c)
    0
  • d)
    Infinity
Correct answer is option 'C'. Can you explain this answer?

Ravi Singh answered
In a pure inductive circuit, current is lagging by 90 degrees from the voltage. The power factor is the cosine of the angle in between the voltage and the current. If the angle between the voltage and current is 90, then cos90=0. Hence, the power factor is zero.

Resonant frequency is when ___________
  • a)
    XL=XC
  • b)
    XL>XC
  • c)
    XL<XC
  • d)
    Cannot be determined
Correct answer is option 'A'. Can you explain this answer?

Rajesh Verma answered
The frequency of a system is said to be resonating when the value of the capacitive reactance and the inductive reactance is the same.

In an RLC series phasor, we start drawing the phasor from which quantity?
  • a)
    Voltage
  • b)
    Resistance
  • c)
    Impedance
  • d)
    Current
Correct answer is option 'D'. Can you explain this answer?

Rithika Pillai answered
In an RLC series phasor diagram, we start drawing the phasor from the quantity which is common to all three components, that is the current.

Find the expression for the current I from the given circuit.
  • a)
    I=IL
  • b)
    I=IR
  • c)
    I=IL+IR
  • d)
    I=0
Correct answer is option 'C'. Can you explain this answer?

Zoya Sharma answered
 I is the total current in the circuit. Since this is a parallel connection, the total current in the circuit is equal to the sum of the currents in each branch of the circuit. Hence I=IR+IL.

In an RLC circuit, the power factor is always ____________
  • a)
    Positive
  • b)
    Negative
  • c)
    Depends on the circuit
  • d)
    Zero
Correct answer is option 'C'. Can you explain this answer?



Power Factor in an RLC Circuit

In an RLC circuit, the power factor is a measure of how effectively the circuit converts electric power into useful work. The power factor of an RLC circuit can vary depending on the components and configuration of the circuit.

Depends on the Circuit

The power factor in an RLC circuit is not always positive, negative, or zero. It depends on the circuit parameters such as the resistance, inductance, and capacitance values, as well as the frequency of the input signal. The power factor can be leading (positive), lagging (negative), or unity (zero) depending on the phase relationship between the voltage and current in the circuit.

Factors Influencing Power Factor

The power factor in an RLC circuit is influenced by several factors:
- The presence of resistance, inductance, and capacitance in the circuit
- The frequency of the input signal
- The phase angle between the voltage and current
- The impedance of the circuit

Calculating Power Factor

The power factor in an RLC circuit can be calculated using the formula:
Power Factor = Cosine(Φ)
Where Φ is the phase angle between the voltage and current in the circuit. The power factor can range from 0 to 1, where 1 represents a perfect unity power factor.

Conclusion

In conclusion, the power factor in an RLC circuit is not always positive, negative, or zero. It depends on the circuit parameters and configuration. By understanding the factors influencing the power factor and calculating it accurately, one can optimize the performance and efficiency of the RLC circuit.

 At resonance, electrostatic energy is ___________ the magnetic energy.
  • a)
    Greater than
  • b)
    Less than
  • c)
    Equal to
  • d)
    Depends on the circuit
Correct answer is option 'C'. Can you explain this answer?

Nitesh Kumar answered
At resonance, the capacitive energy is equal to the inductive energy and the circuit appears to be resistive in nature. The capacitor stores electrostatic energy and the inductor stores magnetic energy hence they are equal.

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