# The following three-phase loads are connected to a short transmission line with impedance per wire of 4 + j7 ohms: Load 1: Resistive load drawing 80 A, Load 2: Capacitor drawing 60 A, Load 3: Inductive load drawing 50 A at 80 %          power factor. What is the sending end      power factor for a receiving end voltage of 34.5 kV?         a. 96 % b. 97 % c. 98 % d. 99 %

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1. The following three-phase loads are connected to a short transmission line with impedance per wire of 4 + j7 ohms: Load 1: Resistive load drawing 80 A, Load 2: Capacitor drawing 60 A, Load 3: Inductive load drawing 50 A at 80 %          power factor. What is the sending end      power factor for a receiving end voltage of 34.5 kV?

a. 96 % b. 97 % c. 98 % d. 99 %

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Step 1

• The power dissipated by the resistive load will be purely active because the power factor is unity.
• There will be reactive power injected by the capacitor.
• Active and reactive power drawn by the inductive load.
Step 2

Step 3

For the short transmission line, the relation between the current is,

The sending end voltage is given by the following expression,

Substitute Z as the transmission line impedance.

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