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A 50 Hz, 3-phase synchronous generator has inductance per phase of 15 mH. The capacitance of generator and circuit beaker is 0.002 mF. What is its natural frequency of oscillation
- a)29 kHz
- b)2.9 kHz
- c)290 kHz
- d)29 MHz
Correct answer is option 'A'. Can you explain this answer?
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A 50 Hz, 3-phase synchronous generator has inductance per phase of 15 ...
To find the natural frequency of oscillation of a 3-phase synchronous generator, we need to consider the inductance and capacitance of the generator and circuit breaker.
1. Inductance per phase:
The given value of inductance per phase is 15 mH (millihenries).
2. Capacitance:
The capacitance of the generator and circuit breaker is given as 0.002 mF (microfarads) or 2 μF.
3. Calculate the natural frequency:
The natural frequency of oscillation can be calculated using the formula:
f = 1 / (2π√(L*C))
Where:
f is the natural frequency in Hz,
L is the inductance in henries,
C is the capacitance in farads, and
π is a mathematical constant approximately equal to 3.14159.
Substituting the given values:
f = 1 / (2π√(0.015 H * 0.002 F))
Simplifying:
f = 1 / (2π√(0.00003))
f = 1 / (2π√3e-5)
f = 1 / (2π * 0.005477)
f ≈ 1 / (0.03438)
f ≈ 29.09 kHz
Therefore, the natural frequency of oscillation of the 3-phase synchronous generator is approximately 29 kHz. Hence, option 'A' is the correct answer.
1. Inductance per phase:
The given value of inductance per phase is 15 mH (millihenries).
2. Capacitance:
The capacitance of the generator and circuit breaker is given as 0.002 mF (microfarads) or 2 μF.
3. Calculate the natural frequency:
The natural frequency of oscillation can be calculated using the formula:
f = 1 / (2π√(L*C))
Where:
f is the natural frequency in Hz,
L is the inductance in henries,
C is the capacitance in farads, and
π is a mathematical constant approximately equal to 3.14159.
Substituting the given values:
f = 1 / (2π√(0.015 H * 0.002 F))
Simplifying:
f = 1 / (2π√(0.00003))
f = 1 / (2π√3e-5)
f = 1 / (2π * 0.005477)
f ≈ 1 / (0.03438)
f ≈ 29.09 kHz
Therefore, the natural frequency of oscillation of the 3-phase synchronous generator is approximately 29 kHz. Hence, option 'A' is the correct answer.
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A 50 Hz, 3-phase synchronous generator has inductance per phase of 15 mH. The capacitance of generator and circuit beaker is 0.002 mF. What is its natural frequency of oscillationa)29 kHzb)2.9 kHzc)290 kHzd)29 MHzCorrect answer is option 'A'. Can you explain this answer?
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