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Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked
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ElectricalPower System
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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

A

Unity

B

0.8 lagging

C

0.8 leading

D

0.6 lagging

Correct Answer

⚙️ TE • Technical Phasor AnalysisElectricalPower System
Option D

0.6 lagging

Quick Summary:

Given: Load voltage VLV_{L}VL​ = 300 V, Load current I = 500 A (resistive load), Line impedance ZlineZ_{line}Zline​ = j0.8 Ω.

📐MAMath SolutionPhasor Analysis
📋 Given

Load voltage VLV_{L}VL​ = 300 V, Load current I = 500 A (resistive load), Line impedance ZlineZ_{line}Zline​ = j0.8 Ω.

🔢 Formula Used

VS=VL+I×ZlineV_S = V_L + I \times Z_{line}VS​=VL​+I×Zline​

📊 Diagram / Illustration
ReIm
VLV_LVL​
I ×Z_lineSending end phasorVₛ
🔢 Step-by-Step Solution
1

Define the load voltage phasor

Since the load is resistive, the load voltage VLV_LVL​ is in phase with the current III. We take VLV_LVL​ as the reference phasor: VL=300+j0V_L = 300 + j0VL​=300+j0 V.

VL=300∠0° VV_L = 300 \angle 0°\text{ V}VL​=300∠0° V

2

Calculate the sending end voltage

The sending end voltage VSV_SVS​ is the sum of the load voltage and the voltage drop across the impedance: VS=VL+I×ZlineV_S = V_L + I \times Z_{line}VS​=VL​+I×Zline​. Here, I=500∠0°I = 500 \angle 0°I=500∠0° A and Zline=j0.8Z_{line} = j0.8Zline​=j0.8 Ω.

VS=300+(500∠0°)(j0.8)=300+j400V_S = 300 + (500 \angle 0°)(j0.8) = 300 + j400VS​=300+(500∠0°)(j0.8)=300+j400

3

Calculate the sending end power factor

The power factor angle ϕS\phi_SϕS​ is the angle of the sending end voltage VSV_SVS​. Since VS=300+j400V_S = 300 + j400VS​=300+j400, the phase angle is tan⁡−1(400300)=tan⁡−1(1.33)=53.13°\tan^{-1}(\frac{400}{300}) = \tan^{-1}(1.33) = 53.13°tan−1(300400​)=tan−1(1.33)=53.13°. The power factor is cos⁡(53.13°)=0.6\cos(53.13°) = 0.6cos(53.13°)=0.6. Since the imaginary component is positive, the current lags the voltage.

cos⁡(ϕS)=cos⁡(tan⁡−1(400300))=0.6 lagging\cos(\phi_S) = \cos(\tan^{-1}(\frac{400}{300})) = 0.6 \text{ lagging}cos(ϕS​)=cos(tan−1(300400​))=0.6 lagging

✅

D is correct because the sending end voltage phasor VS=300+j400V_S = 300 + j400VS​=300+j400 leads the current by an angle whose cosine results in a power factor of 0.6 lagging.

Core Concepts Used
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Phasor addition Transmission line impedance Power factor calculation
💡 EXAM TIP

In power systems, a series inductive reactance always results in a lagging power factor at the sending end relative to the load current.

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