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An inductor is supplied from a sinusoidal voltage source. The magnetic field energy in the inductor changes from peak value to a minimum value of 10 msec. The supply frequency is-
- a)50 Hz
- b)25 Hz
- c)1kHz
- d)100 Hz
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
An inductor is supplied from a sinusoidal voltage source. The magneti...
The frequency of magnetic field energy is twice the supply frequency.
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... T/2 = 2 x [10m]
⇒ T = 40 X 10-3
f = 25Hz
Most Upvoted Answer
An inductor is supplied from a sinusoidal voltage source. The magneti...
The correct answer is option 'B' - 25 Hz.
Explanation:
- The time taken for the magnetic field energy in the inductor to change from peak value to a minimum value is 10 milliseconds.
- This time period is known as the time constant of the inductor, denoted by the symbol 'τ'.
- The time constant is given by the formula τ = L/R, where L is the inductance of the inductor and R is the resistance connected to the inductor.
- In this case, since the inductor is supplied from a sinusoidal voltage source, the resistance connected to the inductor can be assumed to be negligible. Therefore, the time constant is primarily determined by the inductance of the inductor.
- The time constant represents the time taken for the current in the inductor to reach approximately 63.2% of its final value or to decay to approximately 36.8% of its initial value.
- The relationship between the time constant and the frequency of the sinusoidal voltage source can be expressed as τ = 1/(2πf), where f is the frequency of the sinusoidal voltage source.
- Rearranging the formula, we get f = 1/(2πτ).
- Substituting the given time constant of 10 milliseconds (0.01 seconds) into the formula, we get f = 1/(2π*0.01) = 1/(0.0628) ≈ 15.9 Hz.
- Since the supply frequency is the rate at which the voltage source is oscillating, it must be twice the frequency calculated above to account for the full cycle of the sinusoidal waveform. Therefore, the supply frequency is approximately 2 * 15.9 Hz ≈ 31.8 Hz.
- Among the given options, the closest frequency to 31.8 Hz is option 'B' - 25 Hz.
Therefore, the correct answer is option 'B' - 25 Hz.
Explanation:
- The time taken for the magnetic field energy in the inductor to change from peak value to a minimum value is 10 milliseconds.
- This time period is known as the time constant of the inductor, denoted by the symbol 'τ'.
- The time constant is given by the formula τ = L/R, where L is the inductance of the inductor and R is the resistance connected to the inductor.
- In this case, since the inductor is supplied from a sinusoidal voltage source, the resistance connected to the inductor can be assumed to be negligible. Therefore, the time constant is primarily determined by the inductance of the inductor.
- The time constant represents the time taken for the current in the inductor to reach approximately 63.2% of its final value or to decay to approximately 36.8% of its initial value.
- The relationship between the time constant and the frequency of the sinusoidal voltage source can be expressed as τ = 1/(2πf), where f is the frequency of the sinusoidal voltage source.
- Rearranging the formula, we get f = 1/(2πτ).
- Substituting the given time constant of 10 milliseconds (0.01 seconds) into the formula, we get f = 1/(2π*0.01) = 1/(0.0628) ≈ 15.9 Hz.
- Since the supply frequency is the rate at which the voltage source is oscillating, it must be twice the frequency calculated above to account for the full cycle of the sinusoidal waveform. Therefore, the supply frequency is approximately 2 * 15.9 Hz ≈ 31.8 Hz.
- Among the given options, the closest frequency to 31.8 Hz is option 'B' - 25 Hz.
Therefore, the correct answer is option 'B' - 25 Hz.
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An inductor is supplied from a sinusoidal voltage source. The magnetic field energy in the inductor changes from peak value to a minimum value of 10 msec. The supply frequency is-a)50 Hzb)25 Hzc)1kHzd)100 HzCorrect answer is option 'B'. Can you explain this answer?
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