(Solved): 3. The circuit below consists of three loads in series-parallel connection, with each load defined ...

3. The circuit below consists of three loads in series-parallel connection, with each load defined as indicated: \[ \begin{array}{l} \mathrm{Z}_{1}: \mathrm{P}_{1}=100 \mathrm{~W}, \mathrm{Q}_{1}=200 \text { VAR (inductis } \\ \mathrm{Z}_{2}: \mathrm{P}_{2}=400 \mathrm{~W}, \mathrm{pf}=0.8 \text { (leading) } \\ \mathrm{Z}_{3}: \mathrm{P}_{3}=300 \mathrm{~W}, \mathrm{~S}_{3}=600 \mathrm{VA} \end{array} \] Find the overall complex power of the circuit, the overall power factor and the source current in phasor form. Given \( \mathrm{V}_{\mathrm{rms}}=100 \mathrm{~L} 0^{0} \) \[ \begin{array}{r} \text { [6 Marks] } \\ \text { [CO2, PO2, C5] } \end{array} \] 4. Find the value of parallel capacitance needed to correct a load of \( 4 \mathrm{~kW} \) at \( 0.6 \) lagging pf to (i) unity pf (ii) \( 0.9 \) lagging pf. Assume that the load is supplied by a \( 208 \mathrm{~V}_{\text {ms }} \), \( 60 \mathrm{~Hz} \) line.