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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?
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 Inductor Discharging Time Constant
The discharging time constant of an inductor circuit is a crucial concept in electrical engineering. It helps in understanding how quickly the voltage across the inductor decreases when the circuit is opened or the power source is removed.
Discharging Behavior
- When an inductor discharges, the voltage does not drop instantly but follows an exponential decay pattern.
- The time constant (τ) is given by the formula: τ = L/R, where L is the inductance and R is the resistance in the circuit.
Significance of 36.8%
- The voltage across an inductor is described by the equation: V(t) = V0 * e^(-t/τ), where V0 is the initial voltage and e is the base of the natural logarithm.
- After a time period equal to one time constant (τ), the voltage will drop to approximately 36.8% of its initial value (V0).
Why 36.8%?
- The value 36.8% can be derived from the mathematical constant e, which is approximately 2.718.
- At t = τ, the equation simplifies to V(τ) = V0/e, resulting in V(τ) being around 36.8% of V0.
Conclusion
- Therefore, the discharging time constant of a circuit consisting of an inductor is indeed the time taken for the voltage in the inductor to become 36.8% of the initial voltage.
- This understanding is essential for designing and analyzing circuits involving inductors, particularly in applications related to energy storage and timing circuits.
The discharging time constant of an inductor circuit is a crucial concept in electrical engineering. It helps in understanding how quickly the voltage across the inductor decreases when the circuit is opened or the power source is removed.
Discharging Behavior
- When an inductor discharges, the voltage does not drop instantly but follows an exponential decay pattern.
- The time constant (τ) is given by the formula: τ = L/R, where L is the inductance and R is the resistance in the circuit.
Significance of 36.8%
- The voltage across an inductor is described by the equation: V(t) = V0 * e^(-t/τ), where V0 is the initial voltage and e is the base of the natural logarithm.
- After a time period equal to one time constant (τ), the voltage will drop to approximately 36.8% of its initial value (V0).
Why 36.8%?
- The value 36.8% can be derived from the mathematical constant e, which is approximately 2.718.
- At t = τ, the equation simplifies to V(τ) = V0/e, resulting in V(τ) being around 36.8% of V0.
Conclusion
- Therefore, the discharging time constant of a circuit consisting of an inductor is indeed the time taken for the voltage in the inductor to become 36.8% of the initial voltage.
- This understanding is essential for designing and analyzing circuits involving inductors, particularly in applications related to energy storage and timing circuits.
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