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0.6
0.8
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0.8
The problem asks for the power factor given the three-phase reactive power (VAR), line voltage, and line current. However, the calculation shows the reactive power (Q) is 3600 VAR, while the apparent power (S) is S=3тАЛ├ЧVLтАЛ├ЧILтАЛ=3тАЛ├Ч200├Ч(103тАЛ)=3├Ч200├Ч10=6000┬аVA. Given Q=Ssin(╧Х), we have 3600=6000sin(╧Х), which implies sin(╧Х)=0.6, leading to cos(╧Х)=1тИТ0.62тАЛ=0.8.
The problem asks for the power factor given the three-phase reactive power (VAR), line voltage, and line current. However, the calculation shows the reactive power (Q) is 3600 VAR, while the apparent power (S) is S=3тАЛ├ЧVLтАЛ├ЧILтАЛ=3тАЛ├Ч200├Ч(103тАЛ)=3├Ч200├Ч10=6000┬аVA. Given Q=Ssin(╧Х), we have 3600=6000sin(╧Х), which implies sin(╧Х)=0.6, leading to cos(╧Х)=1тИТ0.62тАЛ=0.8.
S=3тАЛVLтАЛILтАЛ тАФ Formula for apparent power in a three-phase system
Q=Ssin(╧Х) тАФ Formula for reactive power
cos(╧Х)=1тИТsin2(╧Х)тАЛ тАФ Relationship between power factor and reactive power factor
In a three-phase system, the total reactive power is given by Q=3тАЛVLтАЛILтАЛsin(╧Х). Here, VLтАЛ=200┬аV and ILтАЛ=103тАЛ┬аA. First, calculate the apparent power S=3тАЛ├Ч200├Ч103тАЛ=6000┬аVA. Then use the power factor angle relationship sin(╧Х)=SQтАЛ=60003600тАЛ=0.6. The power factor is cos(╧Х)=1тИТsin2(╧Х)тАЛ=1тИТ0.36тАЛ=0.8.
Apparent power S is calculated as 6000┬аVA.
Reactive power Q is given as 3600┬аVAR.
The sine of the power factor angle is SQтАЛ=0.6.
The power factor is the cosine of the angle ╧Х.
Standard power measurement technique
Relates real, reactive, and apparent power components
Requires knowledge of phase relationship
Calculation sensitive to input units
Electrical power system analysis
Load characterization in industrial plants
The official answer key suggests Option C (1), but based on standard electrical engineering formulas (Q=3тАЛVLтАЛILтАЛsin╧Х), the result is 0.8. If Q were 0 VAR, the power factor would be 1. Given the provided data of 3600 VAR, 0.8 is the mathematically correct value.
Option B (0.8) is the correct result derived from the problem statement.
B is correct тАФ The calculated power factor based on Q=3600 VAR and S=6000 VA is 0.8.
Always verify if the reactive power Q or the real power P is provided, as mixing P=3тАЛVLтАЛILтАЛcos╧Х and Q=3тАЛVLтАЛILтАЛsin╧Х is a common source of error in exams.
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