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A 415 V, 3-phase voltage is applied to a balanced star connected purely resistive load of 10 тДж. What is the ratio of reactive power to active power?
100
Infinity
1
0
0
In a purely resistive load, the current is in phase with the voltage, resulting in a power factor of 1. Consequently, the reactive power, which is proportional to the sine of the phase angle ╧Х (where ╧Х=0┬░), becomes zero.
In a purely resistive load, the current is in phase with the voltage, resulting in a power factor of 1. Consequently, the reactive power, which is proportional to the sine of the phase angle ╧Х (where ╧Х=0┬░), becomes zero.
P=3тАЛVLтАЛILтАЛcos(╧Х) тАФ Active Power
Q=3тАЛVLтАЛILтАЛsin(╧Х) тАФ Reactive Power
PQтАЛ=tan(╧Х) тАФ Ratio of Reactive Power to Active Power
Reactive power Q is defined as Q=VLтАЛILтАЛsin(╧Х). For a purely resistive load, the impedance angle ╬╕=0┬░, so the phase angle ╧Х=0┬░. Since sin(0┬░)=0, the reactive power consumed by the resistor is null, leading to a ratio of reactive power to active power of 0/P=0.
Purely resistive loads have a power factor of unity.
Inductive or capacitive elements are required to generate reactive power (QюАа=0).
For any purely resistive circuit, ╧Х=0, therefore tan(0)=0.
Unity power factor ensures minimum current for a given power.
No reactive power support required from the source.
Resistive heating is the only form of energy conversion.
Does not support the operation of magnetic flux-based devices like motors.
Electric heaters
Incandescent lighting
Reference standard for calibration
Option A is incorrect because a ratio of 100 implies a highly inductive/capacitive circuit.
Option B is incorrect because infinity implies an open circuit or purely reactive component (P=0).
Option C is incorrect because a ratio of 1 corresponds to a power factor of 0.707 (45┬░ phase angle).
D is correct тАФ The ratio of reactive power to active power for a purely resistive load is tan(0┬░)=0.
Always remember that reactive power (Q) is linked to the energy storage elements (Inductors and Capacitors) and is zero for purely resistive (R) circuits.
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