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In phasor representation of an alternating quantity, the sinusoidally varying alternating quantity can be represented graphically by:
- a)zigzag form
- b)a straight line with an arrow
- c)hyperbolic linear form
- d)a line defining variable points is some distance
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
In phasor representation of an alternating quantity, the sinusoidally ...
Concept:
A phasor is a vector representation of a sinusoidal function that has both a magnitude and a phase angle.
Representations:
Rectangular form: z = x + jy
Polar form: z = r ∠ ϕ
Exponential form: z = z ejϕ
Comparison:
Time Domain: V(t) = Vm cos (ωt + ϕ)
It represents the voltage as a function of time as shown:
Phasor Domain: V = Vm ∠ ϕ
It gives the magnitude and phase and can be represented as:
Where,
Vm is the magnitude of the voltage function
ϕ is the phase angle of the voltage function
Note:
Power factor = cos ϕ
- The phase angle is negative for lagging power factor
- The phase angle is positive for leading power factor
In the phasor representation of an alternating quantity, the sinusoidally varying alternating quantity can be represented graphically by a straight line with an arrow.
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In phasor representation of an alternating quantity, the sinusoidally ...
In the phasor representation of an alternating quantity, the sinusoidally varying alternating quantity can be represented graphically by a straight line with an arrow (option B).
Phasor representation:
A phasor is a vector representation of an alternating quantity, such as voltage or current, that varies sinusoidally with time. It is used to simplify the analysis of AC circuits and allows us to use the tools of vector algebra to solve electrical problems.
Explanation of the answer:
The straight line with an arrow represents the magnitude and phase angle of the alternating quantity in the phasor representation. Here's a detailed explanation of why this representation is correct:
1. Representation of magnitude:
- The length of the straight line represents the magnitude of the alternating quantity. The longer the line, the larger the magnitude of the quantity.
- For example, if we are representing the voltage of an AC circuit, the length of the line represents the magnitude of the voltage.
2. Representation of phase angle:
- The angle between the line and a reference axis represents the phase angle of the alternating quantity.
- The reference axis is usually taken as the horizontal axis, and the angle is measured counterclockwise.
- For example, if the line is at a 30-degree angle with respect to the reference axis, it means that the alternating quantity has a phase angle of 30 degrees.
3. Sinusoidal variation:
- The sinusoidal variation of the alternating quantity is not explicitly represented in the phasor diagram.
- The phasor diagram focuses on representing the magnitude and phase angle of the quantity, rather than the time-varying nature.
- The sinusoidal variation can be understood by considering that the phasor rotates counterclockwise at a constant angular velocity, representing the time-varying nature of the quantity.
Overall, the straight line with an arrow in the phasor representation of an alternating quantity graphically represents the magnitude and phase angle of the quantity. The sinusoidal variation is understood by considering the rotation of the phasor.
Phasor representation:
A phasor is a vector representation of an alternating quantity, such as voltage or current, that varies sinusoidally with time. It is used to simplify the analysis of AC circuits and allows us to use the tools of vector algebra to solve electrical problems.
Explanation of the answer:
The straight line with an arrow represents the magnitude and phase angle of the alternating quantity in the phasor representation. Here's a detailed explanation of why this representation is correct:
1. Representation of magnitude:
- The length of the straight line represents the magnitude of the alternating quantity. The longer the line, the larger the magnitude of the quantity.
- For example, if we are representing the voltage of an AC circuit, the length of the line represents the magnitude of the voltage.
2. Representation of phase angle:
- The angle between the line and a reference axis represents the phase angle of the alternating quantity.
- The reference axis is usually taken as the horizontal axis, and the angle is measured counterclockwise.
- For example, if the line is at a 30-degree angle with respect to the reference axis, it means that the alternating quantity has a phase angle of 30 degrees.
3. Sinusoidal variation:
- The sinusoidal variation of the alternating quantity is not explicitly represented in the phasor diagram.
- The phasor diagram focuses on representing the magnitude and phase angle of the quantity, rather than the time-varying nature.
- The sinusoidal variation can be understood by considering that the phasor rotates counterclockwise at a constant angular velocity, representing the time-varying nature of the quantity.
Overall, the straight line with an arrow in the phasor representation of an alternating quantity graphically represents the magnitude and phase angle of the quantity. The sinusoidal variation is understood by considering the rotation of the phasor.
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In phasor representation of an alternating quantity, the sinusoidally varying alternating quantity can be represented graphically by:a)zigzag formb)a straight line with an arrowc)hyperbolic linear formd)a line defining variable points is some distanceCorrect answer is option 'B'. Can you explain this answer?
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