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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 whichone 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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RLC Series Resonant Circuit
An RLC series resonant circuit consists of a resistor (R), an inductor (L), and a capacitor (C) connected in series. This circuit exhibits resonance when the reactive components cancel each other out, resulting in a purely resistive impedance.
Quality Factor (Q)
The quality factor (Q) of a resonant circuit is a measure of its efficiency. It quantifies the ratio of energy stored in the circuit to the energy dissipated per cycle. It is defined as the ratio of the reactance of the inductor or capacitor to the resistance of the circuit.
Effect on Maximum Stored Energy
When the maximum stored energy in the RLC series resonant circuit is increased by 10%, it means that the energy stored in the inductor and capacitor is increased. This can be achieved by either increasing the inductance or capacitance or by increasing the voltage across the circuit.
Effect on Energy Dissipated per Cycle
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 reducing the current flowing through the circuit.
Relationship between Q, Stored Energy, and Energy Dissipated
The quality factor (Q) of a 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.
Since the maximum stored energy is increased by 10%, the numerator of the Q equation increases, while the denominator remains the same. This results in an increase in the Q factor.
Similarly, since the energy dissipated per cycle is reduced by 10%, the denominator of the Q equation decreases, while the numerator remains the same. This also results in an increase in the Q factor.
Conclusion
Therefore, when the maximum stored energy is increased by 10% and the energy dissipated per cycle is reduced by 10%, it will result in a 22% increase in the quality factor (Q). This can be calculated using the formula:
Percentage increase in Q = (10% increase in stored energy - 10% decrease in energy dissipated) / Q
= (10 - (-10)) / Q
= 20 / Q
= 20 / (1 * Q)
= 20 * 100 / Q
= 2000 / Q
Therefore, the percentage increase in Q is 2000 / Q, which is equal to 22% when Q is approximately 9.09.
Hence, the correct answer is option C, which states that there is a 22% increase in the quality factor.
An RLC series resonant circuit consists of a resistor (R), an inductor (L), and a capacitor (C) connected in series. This circuit exhibits resonance when the reactive components cancel each other out, resulting in a purely resistive impedance.
Quality Factor (Q)
The quality factor (Q) of a resonant circuit is a measure of its efficiency. It quantifies the ratio of energy stored in the circuit to the energy dissipated per cycle. It is defined as the ratio of the reactance of the inductor or capacitor to the resistance of the circuit.
Effect on Maximum Stored Energy
When the maximum stored energy in the RLC series resonant circuit is increased by 10%, it means that the energy stored in the inductor and capacitor is increased. This can be achieved by either increasing the inductance or capacitance or by increasing the voltage across the circuit.
Effect on Energy Dissipated per Cycle
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 reducing the current flowing through the circuit.
Relationship between Q, Stored Energy, and Energy Dissipated
The quality factor (Q) of a 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.
Since the maximum stored energy is increased by 10%, the numerator of the Q equation increases, while the denominator remains the same. This results in an increase in the Q factor.
Similarly, since the energy dissipated per cycle is reduced by 10%, the denominator of the Q equation decreases, while the numerator remains the same. This also results in an increase in the Q factor.
Conclusion
Therefore, when the maximum stored energy is increased by 10% and the energy dissipated per cycle is reduced by 10%, it will result in a 22% increase in the quality factor (Q). This can be calculated using the formula:
Percentage increase in Q = (10% increase in stored energy - 10% decrease in energy dissipated) / Q
= (10 - (-10)) / Q
= 20 / Q
= 20 / (1 * Q)
= 20 * 100 / Q
= 2000 / Q
Therefore, the percentage increase in Q is 2000 / Q, which is equal to 22% when Q is approximately 9.09.
Hence, the correct answer is option C, which states that there is 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 whichone 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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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 whichone 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 Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering 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 whichone 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 Mechanical Engineering 2024 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 whichone 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 whichone 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 Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering 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 whichone 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 Mechanical Engineering 2024 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 whichone 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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