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$$
\begin{array}{l}{\text { The two loads in the circuit shown can be described as follows: }} \\ {\text { Load } 1 \text { absorbs } 8 \mathrm{kW} \text { at a leading p.f. of } 0.8 \text { . }} \\ {\text { Load2 absorbs } 20 \mathrm{kVA} \text { at a lagging p.f. of } \mathrm{O} \text { . } 6 \text { . }} \\ {\text { a) Determine the power factor of the two loads in parallel. }} \\ {\text { b) Determine the apparent power required to supply the loads, }} \\ {\text { the magnitude of the current, } I_{s} \text { , and power loss in T.L. }(0.05+\mathrm{j} 0.5)}\end{array}
$$

Load (1) $$
L_{1} \quad P_{1}=8 K w
$$

$$
PF=0.8
$$    leading     $$
Q=-v e
$$

$$
Q=S \sin \phi=\frac{P}{cos \phi}*\sqrt{1-(PF)^2}
$$

$$
Q=\frac{8000}{0.8} * \sqrt{1-(0.8)^2}=6000 \ VAR
$$

$$
S_{1}=P+J Q=8000-J6000
$$

Load (2) $$
L_{2} \quad  20 \mathrm{KVA}\ , \mathrm{PF}=0.6
$$

$$
P=S \cos \phi=20000 \times 0.6
$$

$$
P=12000 \mathrm{w}
$$

$$
Q=S \sin \phi=20000 \sqrt{1-(0.6)^{2}}
$$

$$
Q=16000 \mathrm{VAR}
$$

$$
S_{2}=P+J Q=12000 +J 16000
$$

$$
\overline{S}_{t o t a l}=\overline{S}_{1}+\overline{S}_{2}=8000-J{6000}+12000+J16000
$$

$$
\overline{S}_{t o t a l}=(20000+J10000) \ VA
$$

$$
I_s^*=\frac{\overline{S}_{total}}{\overline{V}_{r ms}}=\frac{20000+J10000}{250 \ \angle 0}=(80+J40) \ A
$$

$$
\left.I_{s}\right|_{r ms}=(80-J40) A \  , \  |I_{rms}|=\sqrt{(80)^2+(40)^2}=89.44 A
$$

$$
P_{loss}=I^{2} R=(89.44)^2*0.05=400 w
$$

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