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In an RLC series resonant circuit, if the maximum stored energy is increased by 10%and at the same time, the energy dissipated per cycle is reduced by 10%, it will result in which one of the following ?
- a)An 11% decrease in quality factor
- b)An increase in the resonant frequency by 11%
- c)A 22% increase in quality factor
- d)A decrease in the resonance frequency by 22%
Correct answer is option 'C'. Can you explain this answer?
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In an RLC series resonant circuit, if the maximum stored energy is inc...
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In an RLC series resonant circuit, if the maximum stored energy is inc...
Explanation:
To understand why the correct answer is option 'C', let's break down the question and analyze the effects of the given changes on the RLC series resonant circuit.
1. Maximum stored energy increased by 10%:
When the maximum stored energy of the circuit is increased by 10%, it means that the energy stored in the inductor and capacitor at resonance will increase. This can be achieved by either increasing the inductance or the capacitance of the circuit.
2. Energy dissipated per cycle reduced by 10%:
When the energy dissipated per cycle is reduced by 10%, it means that the power loss in the circuit is reduced. This can be achieved by either reducing the resistance or the power factor of the circuit.
Now, let's examine the impact of these changes on the quality factor (Q) and the resonant frequency (ω) of the circuit.
Effect on Quality Factor (Q):
The quality factor of an RLC series resonant circuit is given by the formula Q = ω₀L/R, where ω₀ is the resonant frequency, L is the inductance, and R is the resistance.
- When the maximum stored energy is increased by 10%, it means that the inductance or capacitance of the circuit is increased. As a result, the quality factor will also increase because Q is directly proportional to the inductance.
- When the energy dissipated per cycle is reduced by 10%, it means that the resistance is reduced. This will further increase the quality factor because Q is inversely proportional to the resistance.
Therefore, the combined effect of these changes will result in a significant increase in the quality factor of the circuit.
Effect on Resonant Frequency (ω):
The resonant frequency of an RLC series resonant circuit is given by the formula ω = 1/√(LC), where L is the inductance and C is the capacitance.
- When the maximum stored energy is increased by 10%, it means that the inductance or capacitance of the circuit is increased. As a result, the resonant frequency will decrease because ω is inversely proportional to the square root of the inductance and capacitance.
- When the energy dissipated per cycle is reduced by 10%, it does not have a direct impact on the resonant frequency.
Therefore, the combined effect of these changes will result in a decrease in the resonant frequency of the circuit.
Conclusion:
Based on the analysis above, it can be concluded that the given changes will result in a significant increase in the quality factor (Q) and a decrease in the resonant frequency (ω) of the RLC series resonant circuit. Therefore, the correct answer is option 'C', which states that there will be a 22% increase in the quality factor.
To understand why the correct answer is option 'C', let's break down the question and analyze the effects of the given changes on the RLC series resonant circuit.
1. Maximum stored energy increased by 10%:
When the maximum stored energy of the circuit is increased by 10%, it means that the energy stored in the inductor and capacitor at resonance will increase. This can be achieved by either increasing the inductance or the capacitance of the circuit.
2. Energy dissipated per cycle reduced by 10%:
When the energy dissipated per cycle is reduced by 10%, it means that the power loss in the circuit is reduced. This can be achieved by either reducing the resistance or the power factor of the circuit.
Now, let's examine the impact of these changes on the quality factor (Q) and the resonant frequency (ω) of the circuit.
Effect on Quality Factor (Q):
The quality factor of an RLC series resonant circuit is given by the formula Q = ω₀L/R, where ω₀ is the resonant frequency, L is the inductance, and R is the resistance.
- When the maximum stored energy is increased by 10%, it means that the inductance or capacitance of the circuit is increased. As a result, the quality factor will also increase because Q is directly proportional to the inductance.
- When the energy dissipated per cycle is reduced by 10%, it means that the resistance is reduced. This will further increase the quality factor because Q is inversely proportional to the resistance.
Therefore, the combined effect of these changes will result in a significant increase in the quality factor of the circuit.
Effect on Resonant Frequency (ω):
The resonant frequency of an RLC series resonant circuit is given by the formula ω = 1/√(LC), where L is the inductance and C is the capacitance.
- When the maximum stored energy is increased by 10%, it means that the inductance or capacitance of the circuit is increased. As a result, the resonant frequency will decrease because ω is inversely proportional to the square root of the inductance and capacitance.
- When the energy dissipated per cycle is reduced by 10%, it does not have a direct impact on the resonant frequency.
Therefore, the combined effect of these changes will result in a decrease in the resonant frequency of the circuit.
Conclusion:
Based on the analysis above, it can be concluded that the given changes will result in a significant increase in the quality factor (Q) and a decrease in the resonant frequency (ω) of the RLC series resonant circuit. Therefore, the correct answer is option 'C', which states that there will be a 22% increase in the quality factor.
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In an RLC series resonant circuit, if the maximum stored energy is increased by 10%and at the same time, the energy dissipated per cycle is reduced by 10%, it will result in which one of the following ?a)An 11% decrease in quality factorb)An increase in the resonant frequency by 11%c)A 22% increase in quality factord)A decrease in the resonance frequency by 22%Correct answer is option 'C'. Can you explain this answer? for Mathematics 2025 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about In an RLC series resonant circuit, if the maximum stored energy is increased by 10%and at the same time, the energy dissipated per cycle is reduced by 10%, it will result in which one of the following ?a)An 11% decrease in quality factorb)An increase in the resonant frequency by 11%c)A 22% increase in quality factord)A decrease in the resonance frequency by 22%Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mathematics 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In an RLC series resonant circuit, if the maximum stored energy is increased by 10%and at the same time, the energy dissipated per cycle is reduced by 10%, it will result in which one of the following ?a)An 11% decrease in quality factorb)An increase in the resonant frequency by 11%c)A 22% increase in quality factord)A decrease in the resonance frequency by 22%Correct answer is option 'C'. Can you explain this answer?.
In an RLC series resonant circuit, if the maximum stored energy is increased by 10%and at the same time, the energy dissipated per cycle is reduced by 10%, it will result in which one of the following ?a)An 11% decrease in quality factorb)An increase in the resonant frequency by 11%c)A 22% increase in quality factord)A decrease in the resonance frequency by 22%Correct answer is option 'C'. Can you explain this answer? for Mathematics 2025 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about In an RLC series resonant circuit, if the maximum stored energy is increased by 10%and at the same time, the energy dissipated per cycle is reduced by 10%, it will result in which one of the following ?a)An 11% decrease in quality factorb)An increase in the resonant frequency by 11%c)A 22% increase in quality factord)A decrease in the resonance frequency by 22%Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mathematics 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In an RLC series resonant circuit, if the maximum stored energy is increased by 10%and at the same time, the energy dissipated per cycle is reduced by 10%, it will result in which one of the following ?a)An 11% decrease in quality factorb)An increase in the resonant frequency by 11%c)A 22% increase in quality factord)A decrease in the resonance frequency by 22%Correct answer is option 'C'. Can you explain this answer?.
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