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In P (t) equation, if θ = 0, then P (t) =?
- a)(VmIm/2)(1 + cosωt)
- b)(VmIm/2)(cosωt)
- c)(VmIm/2)(cos2ωt)
- d)(VmIm)(1+cos2ωt)
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
In P (t) equation, if θ = 0, then P (t) =?a)(VmIm/2)(1 + cos&ome...
In P (t) equation, if θ=0⁰, then P (t) =(VmIm/2)(1+cos2ωt). The power wave has a frequency twice that of the voltage or current. Here the average value of power is VmIm/2.
Most Upvoted Answer
In P (t) equation, if θ = 0, then P (t) =?a)(VmIm/2)(1 + cos&ome...
Understanding the Equation P(t)
In the context of electrical engineering, the equation P(t) typically represents the instantaneous power in an AC circuit. The parameters in this equation can vary based on the angle θ, which relates to the phase difference between voltage and current waveforms.
Case When θ = 0
When θ = 0, it denotes that the voltage and current are in phase. This alignment has significant implications for power calculation:
- Voltage (Vm): The maximum voltage.
- Current (Im): The maximum current.
- Frequency (ω): The angular frequency of the AC signal.
Deriving P(t)
The general form of the instantaneous power P(t) in AC circuits is expressed as:
P(t) = Vm * Im * cos(ωt + θ)
With θ set to 0, the equation simplifies to:
P(t) = Vm * Im * cos(ωt)
Now, to find the average power over one complete cycle, we use the relationship that integrates the power over time.
Average Power Calculation
The average power P_avg over one cycle for a cosine function can be represented as:
P_avg = (1/T) ∫ P(t) dt
For the cosine function, the average power simplifies to:
P_avg = (Vm * Im / 2) * (1 + cos(2ωt))
This leads us to the conclusion that when θ = 0, the average power can be expressed as:
P_avg = (Vm * Im)(1 + cos(2ωt))
Conclusion
Thus, the correct answer is option 'D':
P(t) = (VmIm)(1 + cos(2ωt)), which signifies the average power when voltage and current are perfectly in phase.
In the context of electrical engineering, the equation P(t) typically represents the instantaneous power in an AC circuit. The parameters in this equation can vary based on the angle θ, which relates to the phase difference between voltage and current waveforms.
Case When θ = 0
When θ = 0, it denotes that the voltage and current are in phase. This alignment has significant implications for power calculation:
- Voltage (Vm): The maximum voltage.
- Current (Im): The maximum current.
- Frequency (ω): The angular frequency of the AC signal.
Deriving P(t)
The general form of the instantaneous power P(t) in AC circuits is expressed as:
P(t) = Vm * Im * cos(ωt + θ)
With θ set to 0, the equation simplifies to:
P(t) = Vm * Im * cos(ωt)
Now, to find the average power over one complete cycle, we use the relationship that integrates the power over time.
Average Power Calculation
The average power P_avg over one cycle for a cosine function can be represented as:
P_avg = (1/T) ∫ P(t) dt
For the cosine function, the average power simplifies to:
P_avg = (Vm * Im / 2) * (1 + cos(2ωt))
This leads us to the conclusion that when θ = 0, the average power can be expressed as:
P_avg = (Vm * Im)(1 + cos(2ωt))
Conclusion
Thus, the correct answer is option 'D':
P(t) = (VmIm)(1 + cos(2ωt)), which signifies the average power when voltage and current are perfectly in phase.
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In P (t) equation, if θ = 0, then P (t) =?a)(VmIm/2)(1 + cosωt)b)(VmIm/2)(cosωt)c)(VmIm/2)(cos2ωt)d)(VmIm)(1+cos2ωt)Correct answer is option 'D'. 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 In P (t) equation, if θ = 0, then P (t) =?a)(VmIm/2)(1 + cosωt)b)(VmIm/2)(cosωt)c)(VmIm/2)(cos2ωt)d)(VmIm)(1+cos2ωt)Correct answer is option 'D'. 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 In P (t) equation, if θ = 0, then P (t) =?a)(VmIm/2)(1 + cosωt)b)(VmIm/2)(cosωt)c)(VmIm/2)(cos2ωt)d)(VmIm)(1+cos2ωt)Correct answer is option 'D'. Can you explain this answer?.
In P (t) equation, if θ = 0, then P (t) =?a)(VmIm/2)(1 + cosωt)b)(VmIm/2)(cosωt)c)(VmIm/2)(cos2ωt)d)(VmIm)(1+cos2ωt)Correct answer is option 'D'. 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 In P (t) equation, if θ = 0, then P (t) =?a)(VmIm/2)(1 + cosωt)b)(VmIm/2)(cosωt)c)(VmIm/2)(cos2ωt)d)(VmIm)(1+cos2ωt)Correct answer is option 'D'. 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 In P (t) equation, if θ = 0, then P (t) =?a)(VmIm/2)(1 + cosωt)b)(VmIm/2)(cosωt)c)(VmIm/2)(cos2ωt)d)(VmIm)(1+cos2ωt)Correct answer is option 'D'. Can you explain this answer?.
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