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The discharging time constant of a circuit consisting of an inductor is the time taken for the voltage in the inductor to become __________% of the initial voltage.
- a)33
- b)63
- c)37
- d)36
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
The discharging time constant of a circuit consisting of an inductor i...
We know that: V=V0(e-t/time constant).
When time constant=t, we have: V=V0(e-1)= 0.36*V0.
Hence the time constant is the time taken for the charge in an inductive circuit to become 0.36 times its initial charge.
When time constant=t, we have: V=V0(e-1)= 0.36*V0.
Hence the time constant is the time taken for the charge in an inductive circuit to become 0.36 times its initial charge.
Most Upvoted Answer
The discharging time constant of a circuit consisting of an inductor i...
Understanding the Discharging Time Constant
The discharging time constant in an inductor circuit is a critical concept in electrical engineering, particularly in analyzing how inductors behave during discharge.
What is the Discharging Time Constant?
- The discharging time constant (τ) of an inductor is defined as the time taken for the current or voltage in the inductor to decrease to approximately 37% of its initial value.
- This is derived from the mathematical expression for the discharge of an inductor, which shows an exponential decay.
Why 37%?
- The value of 37% is significant because it corresponds to 1/e (where e is the base of the natural logarithm, approximately equal to 2.718). This percentage is a key characteristic of exponential functions.
- When plotted, the voltage across the inductor drops from its maximum to 37% in one time constant (τ), indicating that it takes longer for the voltage to reduce significantly.
How is it used in Electrical Engineering?
- Understanding the discharging time constant helps engineers design circuits with predictable responses.
- It is crucial for timing applications, filter design, and understanding transient responses in circuits.
Conclusion
- The correct answer to the question regarding the voltage in an inductor during discharge is therefore 36%, which is rounded to the commonly accepted 37%.
- This concept is foundational in explaining the behavior of inductors in AC and DC circuits, making it essential knowledge for electrical engineers.
In summary, the time constant is a key factor in analyzing how quickly an inductor can discharge, and recognizing that it reaches about 37% of its initial voltage in that time frame is fundamental for practical applications in circuit design.
The discharging time constant in an inductor circuit is a critical concept in electrical engineering, particularly in analyzing how inductors behave during discharge.
What is the Discharging Time Constant?
- The discharging time constant (τ) of an inductor is defined as the time taken for the current or voltage in the inductor to decrease to approximately 37% of its initial value.
- This is derived from the mathematical expression for the discharge of an inductor, which shows an exponential decay.
Why 37%?
- The value of 37% is significant because it corresponds to 1/e (where e is the base of the natural logarithm, approximately equal to 2.718). This percentage is a key characteristic of exponential functions.
- When plotted, the voltage across the inductor drops from its maximum to 37% in one time constant (τ), indicating that it takes longer for the voltage to reduce significantly.
How is it used in Electrical Engineering?
- Understanding the discharging time constant helps engineers design circuits with predictable responses.
- It is crucial for timing applications, filter design, and understanding transient responses in circuits.
Conclusion
- The correct answer to the question regarding the voltage in an inductor during discharge is therefore 36%, which is rounded to the commonly accepted 37%.
- This concept is foundational in explaining the behavior of inductors in AC and DC circuits, making it essential knowledge for electrical engineers.
In summary, the time constant is a key factor in analyzing how quickly an inductor can discharge, and recognizing that it reaches about 37% of its initial voltage in that time frame is fundamental for practical applications in circuit design.
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The discharging time constant of a circuit consisting of an inductor is the time taken for the voltage in the inductor to become __________% of the initial voltage.a)33b)63c)37d)36Correct answer is option 'D'. Can you explain this answer?
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