Join 60,000+ competitive exam aspirants
A single phase transmission line of Impedance j0.8 Ω supplies a resistive load of 500 A at 300 V. The sending end power factor is
Unity
0.8 lagging
0.8 leading
0.6 lagging
0.6 lagging
Given: Load voltage VL = 300 V, Load current I = 500 A (resistive load), Line impedance Zline = j0.8 Ω.
Load voltage VL = 300 V, Load current I = 500 A (resistive load), Line impedance Zline = j0.8 Ω.
VS=VL+I×Zline
Define the load voltage phasor
Since the load is resistive, the load voltage VL is in phase with the current I. We take VL as the reference phasor: VL=300+j0 V.
VL=300∠0° V
Calculate the sending end voltage
The sending end voltage VS is the sum of the load voltage and the voltage drop across the impedance: VS=VL+I×Zline. Here, I=500∠0° A and Zline=j0.8 Ω.
VS=300+(500∠0°)(j0.8)=300+j400
Calculate the sending end power factor
The power factor angle ϕS is the angle of the sending end voltage VS. Since VS=300+j400, the phase angle is tan−1(300400)=tan−1(1.33)=53.13°. The power factor is cos(53.13°)=0.6. Since the imaginary component is positive, the current lags the voltage.
cos(ϕS)=cos(tan−1(300400))=0.6 lagging
D is correct because the sending end voltage phasor VS=300+j400 leads the current by an angle whose cosine results in a power factor of 0.6 lagging.
In power systems, a series inductive reactance always results in a lagging power factor at the sending end relative to the load current.