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The equation of instantaneous power is?
- a)P (t) = (VmIm/2)(cos(2ωt + θ) + sinθ)
- b)P (t) = (VmIm/2)(sin(2ωt + θ) + cosθ)
- c)P (t) = (VmIm/2)(cos(2ωt + θ) + cosθ)
- d)P (t) = (VmIm/2)(sin(2ωt + θ) + sinθ)
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The equation of instantaneous power is?a)P (t) = (VmIm/2)(cos(2ω...
The equation of instantaneous power is P (t) = (VmIm/2)(cos(2ωt + θ) + cosθ). It consists of two parts. One is a fixed part and the other is time varying which has frequency twice that of the voltage or current wave forms.
Most Upvoted Answer
The equation of instantaneous power is?a)P (t) = (VmIm/2)(cos(2ω...
Understanding Instantaneous Power
Instantaneous power in electrical circuits, particularly in AC systems, is defined as the product of voltage and current at a specific moment in time. For sinusoidal voltages and currents, this can be expressed mathematically.
General Formula
For a voltage V(t) and current I(t) that are sinusoidal:
- V(t) = Vm * cos(ωt + φ)
- I(t) = Im * cos(ωt + θ)
Where:
- Vm and Im are the maximum values of voltage and current,
- ω is the angular frequency,
- φ is the phase angle of voltage,
- θ is the phase angle of current.
Calculating Instantaneous Power
The instantaneous power P(t) can be calculated as:
- P(t) = V(t) * I(t)
Substituting the expressions for V(t) and I(t):
- P(t) = Vm * cos(ωt + φ) * Im * cos(ωt + θ)
Using trigonometric identities, we can simplify this expression.
Why Option C is Correct
In the context of the given options:
- The correct formula for instantaneous power includes terms that result from the multiplication of the sinusoidal functions, including the cosine of the sum of angles.
- The option C formulation captures the behavior of the power over time effectively, demonstrating the influence of both voltage and current phase angles on instantaneous power.
Conclusion
Thus, the correct answer, option C, reflects the proper derivation and relationship of voltage and current in terms of instantaneous power, which can be expressed as:
P(t) = (VmIm/2)(cos(2ωt + (φ + θ)) + cos(φ - θ))
This formula shows how instantaneous power varies with time based on the interactions of voltage and current waveforms.
Instantaneous power in electrical circuits, particularly in AC systems, is defined as the product of voltage and current at a specific moment in time. For sinusoidal voltages and currents, this can be expressed mathematically.
General Formula
For a voltage V(t) and current I(t) that are sinusoidal:
- V(t) = Vm * cos(ωt + φ)
- I(t) = Im * cos(ωt + θ)
Where:
- Vm and Im are the maximum values of voltage and current,
- ω is the angular frequency,
- φ is the phase angle of voltage,
- θ is the phase angle of current.
Calculating Instantaneous Power
The instantaneous power P(t) can be calculated as:
- P(t) = V(t) * I(t)
Substituting the expressions for V(t) and I(t):
- P(t) = Vm * cos(ωt + φ) * Im * cos(ωt + θ)
Using trigonometric identities, we can simplify this expression.
Why Option C is Correct
In the context of the given options:
- The correct formula for instantaneous power includes terms that result from the multiplication of the sinusoidal functions, including the cosine of the sum of angles.
- The option C formulation captures the behavior of the power over time effectively, demonstrating the influence of both voltage and current phase angles on instantaneous power.
Conclusion
Thus, the correct answer, option C, reflects the proper derivation and relationship of voltage and current in terms of instantaneous power, which can be expressed as:
P(t) = (VmIm/2)(cos(2ωt + (φ + θ)) + cos(φ - θ))
This formula shows how instantaneous power varies with time based on the interactions of voltage and current waveforms.
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The equation of instantaneous power is?a)P (t) = (VmIm/2)(cos(2ωt + θ) + sinθ)b)P (t) = (VmIm/2)(sin(2ωt + θ) + cosθ)c)P (t) = (VmIm/2)(cos(2ωt + θ) + cosθ)d)P (t) = (VmIm/2)(sin(2ωt + θ) + sinθ)Correct answer is option 'C'. Can you explain this answer? for Electrical Engineering (EE) 2025 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about The equation of instantaneous power is?a)P (t) = (VmIm/2)(cos(2ωt + θ) + sinθ)b)P (t) = (VmIm/2)(sin(2ωt + θ) + cosθ)c)P (t) = (VmIm/2)(cos(2ωt + θ) + cosθ)d)P (t) = (VmIm/2)(sin(2ωt + θ) + sinθ)Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The equation of instantaneous power is?a)P (t) = (VmIm/2)(cos(2ωt + θ) + sinθ)b)P (t) = (VmIm/2)(sin(2ωt + θ) + cosθ)c)P (t) = (VmIm/2)(cos(2ωt + θ) + cosθ)d)P (t) = (VmIm/2)(sin(2ωt + θ) + sinθ)Correct answer is option 'C'. Can you explain this answer?.
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