Question

Two industrial loads each require 250∠0 V (rms) at 60Hz. Load 1 absorbs 8kW at 0.8 leading; load 2 absorbs 20kVa at 0.6 lagging l. The line that transmits the power from the source to the load has an impedance of (0.05 + j0.5) Ohm

a. Sketch the circuit
b. find complex power for the line and the load
c. Power (complex) supply by the source (proof the sums of all power equal to zero)

Answer 1

Ans)

a)

The sketch of circuit is

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b)

Load 1: given

Now complex power is

negative sign for reactive power for leading powerfactor

The current through load 1 is

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Load 2  

The complex power is

the current through laod 2 is

total current through the line is

Total complex power of the load is

Total complex power of transmission line is

where Vt=I*Zt voltage across transmission line

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c)

Power supply by source is