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If the voltage across and the current into a certain load or part of the circuit are expressed by I = |I|∠β, respectively. Reactive power (VI*) will be ___________ when the phase angle ∠(α - β) and current is __________
- a)positive, positive
- b)negative, negative
- c)negative, positive
- d)positive, negative
Correct answer is option 'A'. Can you explain this answer?
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If the voltage across and the current into a certain load or part of t...
Complex Power:
Considered a circuit in which supply voltage, V ∠α and current, I ∠β and impedance Z,
Complex Power (S) = VI*
S = (V ∠+α) (I ∠-β) = VI ∠(α - β)
Considered, (α - β) = ϕ
S = VI (cos ϕ + j sin ϕ) …. (1)
And, S = P + jQ …. (2)
From equation (1) and (2),
P = VI cos ϕ
Q = VI sin ϕ
The phasor diagram of the circuit can be drawn as,
From the phasor, we can say the load is inductive,
- Inductive load has the property of absorbing reactive power by the load, therefore reactive power (Q) is positive.
- From the phasor it is clear that the voltage leads the current, therefore the phase angle between the voltage and current (α - β) is positive.
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If the voltage across and the current into a certain load or part of t...
Understanding Reactive Power
Reactive power (measured in VARs) is a crucial concept in AC circuits, representing the power that alternates between the source and load but does not perform any real work. It arises from the phase difference between voltage and current.
Voltage and Current Representation
- The voltage across the load can be expressed as:
**V = |V|∠α**
- The current into the load is expressed as:
**I = |I|∠β**
Here, α and β are the phase angles of voltage and current, respectively.
Calculating Reactive Power
Reactive power (Q) is calculated as:
**Q = V * I* = |V| * |I| * sin(α - β)**
Where:
- **V** is the voltage magnitude
- **I*** is the complex conjugate of the current
The sine function indicates the significance of the phase angle difference (α - β).
Analyzing the Phase Angles
- When **α - β > 0** (meaning α is greater than β), **sin(α - β)** is positive, resulting in positive reactive power.
- Conversely, when **α - β < 0**,="" it="" yields="" negative="" reactive="" power.="" />
Conclusion: The Correct Answer
In the context of the question:
- If the phase angle **α - β** is positive and the current **|I|** is also positive, it indicates that the circuit is absorbing reactive power, which confirms that the correct answer is:
**a) positive, positive**
This illustrates that the load is primarily inductive, drawing reactive power from the source.
Reactive power (measured in VARs) is a crucial concept in AC circuits, representing the power that alternates between the source and load but does not perform any real work. It arises from the phase difference between voltage and current.
Voltage and Current Representation
- The voltage across the load can be expressed as:
**V = |V|∠α**
- The current into the load is expressed as:
**I = |I|∠β**
Here, α and β are the phase angles of voltage and current, respectively.
Calculating Reactive Power
Reactive power (Q) is calculated as:
**Q = V * I* = |V| * |I| * sin(α - β)**
Where:
- **V** is the voltage magnitude
- **I*** is the complex conjugate of the current
The sine function indicates the significance of the phase angle difference (α - β).
Analyzing the Phase Angles
- When **α - β > 0** (meaning α is greater than β), **sin(α - β)** is positive, resulting in positive reactive power.
- Conversely, when **α - β < 0**,="" it="" yields="" negative="" reactive="" power.="" />
Conclusion: The Correct Answer
In the context of the question:
- If the phase angle **α - β** is positive and the current **|I|** is also positive, it indicates that the circuit is absorbing reactive power, which confirms that the correct answer is:
**a) positive, positive**
This illustrates that the load is primarily inductive, drawing reactive power from the source.
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If the voltage across and the current into a certain load or part of the circuit are expressed by I = |I|∠β, respectively. Reactive power (VI*) will be ___________ when the phase angle ∠(α - β) and current is __________a)positive, positiveb)negative, negativec)negative, positived)positive, negativeCorrect answer is option 'A'. Can you explain this answer?
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