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**Competitive ****Resonance in AC Circuits MCQs ( Electrical Engineering ) MCQs – ****Electrical Engineering MCQs**

#### Latest Electrical Engineering MCQs

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**Resonance in AC Circuits MCQs ( Electrical Engineering ) MCQs – ****Electrical Engineering MCQs**

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# Frequency Variation in a Series RLC Circuit

**1. 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**Answer: b****Explanation: We know that Quality factor is equal to the resonant frequency divided by the bandwidth.****Q=f _{res}/Bandwidth = 50/1 = 50.**

**2. What is the SI unit for quality factor?**

a) Hz

b) kHz

c) MHz

**d) No unit**

**Answer: d**

**Explanation: We know that Quality factor is equal to the resonant frequency divided by the bandwidth. It is one frequency divided by another hence it has no unit.**

**3. What happens to the quality factor when the bandwidth increases?**

a) Increases

**b) Decreases**

c) Remains the same

d) Becomes zero

**Answer: b**

**Explanation: Q=f**

_{res}/Bandwidth**Quality factor is inversely proportional to bandwidth. So, if bandwidth increases quality factor decreases.**

**4. What happens to the quality factor when resonant frequency increases?**

**a) Increases**

b) Decreases

c) Remains the same

d) Becomes zero

**Answer: a**

**Explanation: Q=f**

_{res}/Bandwidth**Quality factor is directly proportional to resonant frequency. So, if resonant frequency increases quality factor increases.**

**5. Resonance frequency occurs when __________________**

**a) X**

_{L}=X_{C}b) X

_{L}>X

_{C}

c) X

_{L}<X

_{C}

d) Cannot be determined

**Answer: a**

**Explanation: The frequency of a system is said to be resonating when the value of the capacitive reactance and the inductive reactance is the same.**

**6. The current leads the supply voltage in a series RLC circuit has its frequency _________ the resonant frequency.**

a) Above

**b) Below**

c) Equal to

d) Cannot be determined

**Answer: b**

**Explanation: Current is leading the voltage indicates capacitor dominating circuit. X**

_{C}>X_{L}=> 1/(ωC) > ωL => ω<1/√LC**So, frequency less than resonant frequency.**

**7. What is the power factor of a series RLC circuit under resonance condition?**

a) 0

**b) 1**

c) Infinity

d) 100

**Answer: b**

**Explanation: The power factor for a series RLC circuit in resonance condition is always unity because the current is in phase with the voltage under resonance condition.**

**Φ=0**

^{0}=> cos ϕ = 1 i.e. power factor = 1.**8. The current lags the supply voltage in a series RLC circuit has its frequency _________ the resonant frequency.**

**a) Above**

b) Below

c) Equal to

d) Cannot be determined

**Answer: a**

**Explanation: Current is lagging the voltage indicates inductor dominating circuit. X**

_{C}< X_{L}=> 1/(ωC) < ωL => ω > 1/√LC**So, frequency more than resonant frequency.**

**9. What is the correct formula for quality factor?**

a) Q=BW*fr

b) Q=BW/fr

**c) Q=fr/BW**

d) Q=fr2

**Answer: c**

**Explanation: 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.**

# Quality Factor

**1. Quality factor is also known as _________****a) Voltage magnification**

b) Current magnification

c) Resistance magnification

d) Impedance magnification**Answer: a****Explanation: 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.****2. At resonance condition, the voltage across the capacitor and inductor is _________ the source voltage.****a) Greater than**

b) Less than

c) Equal to

d) Much less than**Answer: a****Explanation: In resonance condition, the voltage across the capacitor and inductor is greater than the source voltage because the voltage across the capacitor or inductor in resonance condition is equal to Q times the source voltage.****3. What is the voltage across the capacitor when the source voltage is 100V and the Q factor is 10?**

a) 100V

b) 10V**c) 1000V**

d) 0V**Answer: c****Explanation: We know that voltage across the capacitor in resonance condition is equal to Q times the source voltage.****Q=V _{C}/V_{S} where V_{C} is capacitive voltage and V_{S} is source voltage.**

**10=V**

_{C}/100**V**

_{C}=1000 V.**4. Find the Q factor when the voltage across the capacitor is 1000V and the source voltage is 100V.**

**a) 10**

b) 20

c) 30

d) 40

**Answer: a**

**Explanation: We know that voltage across the capacitor in resonance condition is equal to Q times the source voltage.**

**Q=V**

_{C}/V_{S}where V_{C}is capacitive voltage and V_{S}is source voltage. Q=1000/100 = 10 V.**5. Find the source voltage when the voltage across the capacitor is 1000V and the Q factor is 10.**

a) 10V

b) 200V

**c) 100V**

d) 90V

**Answer: c**

**Explanation: We know that voltage across the capacitor in resonance condition is equal to Q times the source voltage.**

**Q=V**

_{C}/V_{S}where V_{C}is capacitive voltage and V_{S}is source voltage. 10=1000/V_{S}**V**

_{S}=100 V.**6. What is the voltage across the inductor when the source voltage is 200V and the Q factor is 10?**

a) 100V

b) 20V

**c) 2000V**

d) 0V

**Answer: c**

**Q=V**

_{L}/V_{S}where V_{L}is inductive voltage and V_{S}is source voltage. 10=V_{L}/200 => V_{L}= 2000 V.**7. Find the Q factor when the voltage across the inductor is 2000V and the source voltage is 100V.**

a) 10

**b) 20**

c) 30

d) 40

**Answer: b**

**Q=V**

_{L}/V_{S}where V_{L}is inductive voltage and V_{S}is source voltage. Q=2000/100=20.**8. Find the source voltage when the voltage across the inductor is 2000V and the Q factor is 20.**

a) 10V

b) 200V

**c) 100V**

d) 90V

**Answer: c**

**Q=V**

_{L}/V_{S}where V_{L}is inductive voltage and V_{S}is source voltage.**20=2000/V**

_{S}**V**

_{S}=100 V.**9. What happens to the voltage across the capacitor when the Q factor increases?**

**a) Increases**

b) Decreases

c) Remains the same

d) Becomes zero

**Answer: a**

**Explanation: 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.**

**10. What happens to the voltage across the inductor when the Q factor decreases?**

a) Increases

**b) Decreases**

c) Remains the same

d) Becomes zero

**Answer: b**

**Explanation: 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.**

# Oscillation of Energy at Resonance

**1. The energy stored in the capacitor is of _________ nature.****a) Electrostatic**

b) Magnetic

c) Neither electrostatic nor magnetic

d) Either electrostatic or magnetic**Answer: a****Explanation: Since capacitor stores charge in between the plates and energy associated with static charge is of electrostatic nature, so we can say energy stored in the capacitor is of electrostatic nature.****2. The energy stored in the inductor is of _________ nature.**

a) Electrostatic**b) Magnetic**

c) Neither electrostatic nor magnetic

d) Either electrostatic or magnetic**Answer: b****Explanation: Since inductor stores current which involves moving charge and energy associated with moving charge is of magnetic nature so we can say energy stored in the inductor is of magnetic nature.****3. At resonance, the circuit appears __________**

a) Inductive

b) Capacitive

c) Either inductive or capacitive**d) Resistive****Answer: d****Explanation: At resonance, the circuit appears resistive because the capacitive and inductive energies are equal to each other.****4. At resonance, the capacitive energy is ___________ inductive energy.**

a) Greater than

b) Less than**c) Equal to**

d) Depends on the circuit**Answer: c****Explanation: At resonance, energy stored in the capacitor is equal to energy stored in the inductor because capacitive reactance and inductive reactance are equal at resonance. So, at resonance, capacitive energy is equal to inductive energy.****5. At resonance, electrostatic energy is ___________ the magnetic energy.**

a) Greater than

b) Less than**c) Equal to**

d) Depends on the circuit**Answer: c****Explanation: At resonance, energy stored in the capacitor is equal to energy stored in the inductor because capacitive reactance and inductive reactance are equal at resonance. The capacitor stores electrostatic energy and the inductor stores magnetic energy hence they are equal.**

**6. The maximum magnetic energy stored in an inductor at any instance is?****a) E=LI _{m}^{2}/2**

b) E=LI

_{m}/2

c) E=LI

_{m}

^{2}

d) E=LI

_{m}

^{2}*2

**Answer: a**

**Explanation: At any instant, the magnetic energy stored in an inductor is E=LI**

_{m}^{2}/2, where I_{m}is the maximum current and L is the value of the inductor.**7. The maximum electrostatic energy stored in a capacitor at any instance is?**

a) CV

_{m}

^{2}

**b) 1/2*CV**

_{m}^{2}c) CV

_{m}

d) CV

_{m}/2

**Answer: b**

**Explanation: The maximum electrostatic energy stored in a capacitor at any instance is 1/2*CV**

_{m}^{2}, where C is the capacitance value and V_{m}is the peak voltage.**8. Q is the ratio of?**

a) Active power to reactive power

b) Reactive power to active power

**c) Reactive power to average power**

d) Reactive power to capacitive power

**Answer: c**

**Explanation: Q is the ratio of the reactive power to the average power. The reactive power is due to the inductance or capacitance and the average power is due to the resistance.**

**9. 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

**Answer: c**

**Explanation: Q is the ratio of the reactive power to the average power.**

**Q = Reactive power / Average power = 10/5 = 2.**

**10. Find the reactive power when the average power is 5W and Q=2.**

**a) 10W**

b) 5W

c) 2W

d) 1W

**Answer: a**

**Explanation: Q is the ratio of the reactive power to the average power.**

**Q = Reactive power / Average power**

**2 = Reactive power / 5**

**Reactive Power = 2*5 = 10W.**

# Bandwidth

**1. The SI unit for bandwidth is?****a) Hz**

b) Watt

c) kHz

d) kW**Answer: a****Explanation: The SI unit for bandwidth is Hz. Hertz is the SI unit because bandwidth is basically frequency and the unit for frequency is Hz.****2. At bandwidth frequency range, the value of the current I is?**

a) I=Im/2

b) I=Im^{2}

c) I=Im**d) I=Im/√2****Answer: d****Explanation: At the bandwidth frequency range, the value of the current is equal to the maximum value of current divided by √2.****3. At bandwidth frequency range, the value of the voltage V is?**

a) V=Vm/2

b) V=Vm^{2}

c) V=Vm**d) V=Vm/√2****Answer: d****Explanation: At the bandwidth frequency range, the value of the voltage is equal to the maximum value of voltage divided by √2.****4. At resonance, bandwidth includes the frequency range that allows _____ percent of the maximum current to flow.**

a) 33.33

b) 66.67

c) 50**d) 70.7****Answer: d****Explanation: At resonance, bandwidth includes the frequency range that allows 70.2 percent of the maximum current to flow. This is because in the bandwidth frequency range, the value of the current is equal to the maximum value of current divided by √2.****5. 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****Answer: d****Explanation: At resonance, bandwidth includes the frequency range that allows 70.2 percent of the maximum voltage to flow. This is because in the bandwidth frequency range, the value of the voltage is equal to the maximum value of voltage divided by √2.****6. Find the value of current in the bandwidth range when the maximum value of current is 50A.**

a) 56.65A**b) 35.36A**

c) 45.34A

d) 78.76A**Answer: b****Explanation: 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.****7. Find the value of voltage in the bandwidth range when the maximum value of voltage is 100 V.**

a) 56.65 V

b) 35.36 V

c) 45.34 V**d) 70.72 V****Answer: d****Explanation: At the bandwidth frequency range, the value of the voltage is equal to the maximum value of voltage divided by √2. Hence V =100/√2= 70.72V.****8. Bandwidth is the difference of_____________________ frequencies.****a) half power**

b) full power

c) double power

d) wattless**Answer: a****Explanation: Current for the end frequencies of bandwidth is 1/√2 times the maximum current. So, power at the end frequencies of bandwidth is half the maximum power. So, bandwidth is the difference of half power frequencies.****9. For a sharp resonance, bandwidth is ______________****a) low**

b) high

c) zero

d) infinity**Answer: a****Explanation: For sharp resonance quality factor is high and the quality factor is inversely proportional to bandwidth so bandwidth is low for sharp resonance.****10. Current is maximum at __________ frequency of bandwidth.**

a) left end**b) middle**

c) right end

d) all end**Answer: b****Explanation: Current will be maximum at a frequency which is at the middle of bandwidth.****On both sides, it decreases and is 1/√2 times the maximum current at the ends of bandwidth.**

# Selectivity

**1. Shape of the resonance curve depends upon the?****a) Q-factor**

b) Voltage

c) Current

d) Either voltage or current**Answer: a****Explanation: The shape of the resonance curve depends on the Q factor because of the equation:****Q=Resonance frequency / Bandwidth. Sharp resonance means high quality factor.****2. A circuit is said to be selective if it has a _____ peak and ____ bandwidth.**

a) Blunt, narrow**b) Sharp, narrow**

c) Sharp, broad

d) Blunt, broad**Answer: b****Explanation: For a circuit to be selective, it should have high quality factor. And we know that for high quality factor, resonance frequency should be high(peak should be sharp) and bandwidth should be narrow.**

Capacitance And Capacitors MCQs

**3. What is the Q factor of a selective circuit?**

a) Very low**b) Very high**

c) Zero

d) Infinity**Answer: b****Explanation: For a circuit to be selective, it should have high quality factor. It should have a sharp peak with narrow bandwidth.****4. In selective circuits, higher the Q factor _________ the peak.****a) Sharper**

b) Blunter

c) Neither sharper nor blunter

d) Either sharper or blunter**Answer: a****Explanation: Q=Resonance frequency / Bandwidth.****Higher the quality factor, sharper the peak of resonance curve.****5. Q is a measure of _________**

a) Resonance

b) Bandwidth**c) Selectivity**

d) Either resonance or bandwidth**Answer: c****Explanation: For a circuit to be selective, it should have a high quality factor. It should have a sharp peak with narrow bandwidth.****6. In selective circuits, the resonant frequency lies in the ________ of the bandwidth frequency range.**

a) Beginning

b) End**c) Midpoint**

d) Cannot be determined**Answer: c****Explanation: In selective circuits, the resonant frequency lies in the midpoint of the bandwidth frequency range.****7. In order for high selectivity, the resistance must be?****a) Small**

b) Large

c) Negative

d) Positive**Answer: a****Explanation: For high selectivity, the Q factor should be large and for Q factor to be large, the resistance would be small because Q is inversely proportional to the resistance.**

# Voltages in a Series RLC Circuit

**1. In a series RLC circuit, the phase difference between the voltage across the capacitor and the voltage across the resistor is?**

a) 0^{0}**b) 90 ^{0}**

c) 180

^{0}

d) 360

^{0}

**Answer: b**

**Explanation: In a series RLC circuit, voltage across capacitor lag the current by 900 and voltage across resistor is in phase with current so, the phase difference between the voltage across the capacitor and the voltage across the resistor is 900.**

**2. In a series RLC circuit, the phase difference between the voltage across the inductor and the voltage across the resistor is?**

a) 0

^{0}

**b) 90**

^{0}c) 180

^{0}

d) 360

^{0}

**Answer: b**

**Explanation: In a series RLC circuit, voltage across inductor lead the current by 90**

^{0}and voltage across resistor is in phase with current so, the phase difference between the voltage across the inductor and the voltage across the resistor is 90^{0}.**3. In a series RLC circuit, the phase difference between the voltage across the capacitor and the voltage across the inductor is?**

a) 0

^{0}

b) 90

^{0}

**c) 180**

^{0}d) 360

^{0}

**Answer: c**

**Explanation: In a series RLC circuit, voltage across inductor lead the current by 90**

^{0}and voltage across capacitor lag the current by 900 so, the phase difference between the voltage across the inductor and the voltage across the capacitor is 180^{0}.**4. In a series RLC circuit, the phase difference between the voltage across the resistor and the current in the circuit is?**

**a) 0**

^{0}b) 90

^{0}

c) 180

^{0}

d) 360

^{0}

**Answer: a**

**Explanation: In a series RLC circuit, the phase difference between the voltage across the resistor and the current in the circuit is 0 degrees because they are in phase.**

**5. In a series RLC circuit, the phase difference between the voltage across the capacitor and the current in the circuit is?**

a) 0

^{0}

**b) 90**

^{0}c) 180

^{0}

d) 360

^{0}

**Answer: b**

**Explanation: In a series RLC circuit, voltage across capacitor lag the current by 90**

^{0}so, the phase difference between the voltage across the capacitor and current is 90^{0}.**6. In a series RLC circuit, the phase difference between the voltage across the inductor and the current in the circuit is?**

a) 0

^{0}

**b) 90**

^{0}c) 180

^{0}

d) 360

^{0}

**Answer: b**

**Explanation: In a series RLC circuit, voltage across inductor lead the current by 90**

^{0}so, the phase difference between the voltage across the inductor and the current is 90^{0}.**7. The current in the inductor lags the voltage in a series RLC circuit ___________ resonant frequency.**

**a) Above**

b) Below

c) Equal to

d) Depends on the circuit

**Answer: a**

**Explanation: The current in the inductor lags the voltage in a series RLC circuit if circuit is inductive dominant i.e. if X**

_{L}> X_{C}ωL > 1/ωC => ω > 1/√LC => ω > ω_{0}. So, the current in the inductor lags the voltage in a series RLC circuit above the resonant frequency.**8. The current in the capacitor leads the voltage in a series RLC circuit ___________ resonant frequency.**

a) Above

**b) Below**

c) Equal to

d) Depends on the circuit

**Answer: b**

**Explanation: The current in the capacitor leads the voltage in a series RLC circuit if circuit is capacitive dominant i.e. if X**

_{L}< X_{C}**ωL < 1/ωC => ω < 1/√LC => ω < ω**

_{0}. So, the current in the capacitor leads the voltage in a series RLC circuit below the resonant frequency.**9. The current in the inductor ___________ the voltage in a series RLC circuit above the resonant frequency.**

a) Leads

**b) Lags**

c) Equal to

d) Depends on the circuit

**Answer: b**

**Explanation: ω > ω**

_{0}=> ω > 1/√LC**=> ωL > 1/ωC => X**

_{L}> X_{C}**The circuit is inductive dominant so, the current in the inductor lags the voltage in a series RLC circuit above the resonant frequency.**

**10. The current in the capacitor ___________ the voltage in a series RLC circuit below the resonant frequency.**

**a) Leads**

b) Lags

c) Equal to

d) Depends on the circuit

**Answer: a**

**Explanation: ω < ω**

_{0}=> ω < 1/√LC**=> ωL < 1/ωC => X**

_{L}< X_{C}The circuit is capacitive dominant so, the current in the capacitor leads the voltage in a series RLC circuit above the resonant frequency.# The Current in a Series RLC Circuit

**1. In a series RLC circuit, the phase difference between the current in the capacitor and the current in the resistor is?****a) 0 ^{0}**

b) 90

^{0}

c) 180

^{0}

d) 360

^{0}

**Answer: a**

**Explanation: In a series RLC circuit, the phase difference between the current in the capacitor and the current in the resistor is 0**

^{0}because same current flows in the capacitor as well as the resistor.**2. In a series RLC circuit, the phase difference between the current in the inductor and the current in the resistor is?**

**a) 0**

^{0}b) 90

^{0}

c) 180

^{0}

d) 360

^{0}

**Answer: a**

**Explanation: In a series RLC circuit, the phase difference between the current in the inductor and the current in the resistor is 0**

^{0}because same current flows in the inductor as well as the resistor.**3. In a series RLC circuit, the phase difference between the current in the capacitor and the current in the inductor is?**

**a) 0**

^{0}b) 90

^{0}

c) 180

^{0}

d) 360

^{0}

**Answer: a**

**Explanation: In a series RLC circuit, the phase difference between the current in the inductor and the current in the capacitor is 0**

^{0}because same current flows in the inductor as well as the capacitor.**4. In a series RLC circuit, the phase difference between the current in the circuit and the voltage across the resistor is?**

**a) 0**

^{0}b) 90

^{0}

c) 180

^{0}

d) 360

^{0}

**Answer: a**

**Explanation: In a series RLC circuit, the phase difference between the voltage across the resistor and the current in the circuit is 0**

^{0}because they are in phase.**5. In a series RLC circuit, the phase difference between the current in the circuit and the voltage across the capacitor is?**

a) 0

^{0}

**b) 90**

^{0}c) 180

^{0}

d) 360

^{0}

**Answer: b**

**Explanation: In a series RLC circuit, voltage across capacitor lags the current in the circuit by 90**

^{0}so, the phase difference between the voltage across the capacitor and the current in the circuit is 90^{0}.**6. _________ the resonant frequency, the current in the inductor lags the voltage in a series RLC circuit.**

**a) Above**

b) Below

c) Equal to

d) Depends on the circuit

**Answer: a**

**Explanation: The current in the inductor lags the voltage in a series RLC circuit if a circuit is inductive dominant i.e. if X**

_{L}> X_{C}**ω**

_{L}> 1/ω_{C}=> ω > 1/√LC => ω > ω_{0}.**So, the current in the inductor lags the voltage in a series RLC circuit above the resonant frequency.**

**7. _________ the resonant frequency, the current in the capacitor leads the voltage in a series RLC circuit.**

a) Above

**b) Below**

c) Equal to

d) Depends on the circuit

**Answer: b**

**Explanation: The current in the capacitor leads the voltage in a series RLC circuit if circuit is capacitive dominant i.e.i.e. if X**

_{L}< X_{C}**ω**

_{L}< 1/ω_{C}=> ω < 1/√LC => ω < ω_{0}.**So, the current in the capacitor leads the voltage in a series RLC circuit below the resonant frequency.**