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A 3-phase voltage of 220 V is applied to a balanced, delta-connected, 3-phase, purely resistive load. Calculate the ratio of the reactive power to the active power.
0
1
0.5
2
0
In a purely resistive circuit, the voltage and current are in phase with each other. Consequently, the phase angle ╧Х is 0┬░, resulting in a power factor of cos(0┬░)=1.
In a purely resistive circuit, the voltage and current are in phase with each other. Consequently, the phase angle ╧Х is 0┬░, resulting in a power factor of cos(0┬░)=1.
P=3тАЛVLтАЛILтАЛcos(╧Х) тАФ Active power calculation
Q=3тАЛVLтАЛILтАЛsin(╧Х) тАФ Reactive power calculation
PQтАЛ=tan(╧Х) тАФ Ratio of reactive to active power
Reactive power (Q) is defined by the formula Q=VLтАЛILтАЛsin(╧Х). For a purely resistive load, the power factor angle ╧Х is 0, and since sin(0)=0, the reactive power consumed by the load is always zero regardless of the circuit configuration (star or delta).
A purely resistive load does not store energy in magnetic or electric fields.
The reactive power is non-zero only in circuits containing inductors or capacitors.
The ratio of reactive power to active power is equivalent to the tangent of the impedance angle, tan(╧Х).
For pure resistance, ╧Х=0, hence tan(0)=0.
Unity power factor minimizes current for a given real power delivery.
No reactive power support required from the utility grid.
Purely resistive loads are rare in industrial motors or inductive equipment.
Higher heating losses occur compared to highly inductive systems.
Electric heating elements
Incandescent lighting systems
Calibration of power measurement instruments
Since tan(0)=0, the ratio of reactive power (Q) to active power (P) is 0.
Option B (1) would correspond to a load where the phase angle is 45┬░ (i.e., tan(45┬░)=1).
A is correct тАФ For a purely resistive load, the phase angle is 0┬░, making the reactive power 0 and the ratio Q/P=0.
Always remember that in AC circuits, the presence of purely resistive components implies ╧Х=0, whereas pure inductors imply ╧Х=90┬░ and pure capacitors imply ╧Х=тИТ90┬░.
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