(Solved):   (b) An equivalent circuit of a power system consists of voltage supply, \( \mathrm{V}_{\ma ...

 

(b) An equivalent circuit of a power system consists of voltage supply, \( \mathrm{V}_{\mathrm{s}}=400 \mathrm{~V}_{\mathrm{rms}} \) and frequency of \( 50 \mathrm{~Hz} \), respectively is supplying various loads as illustrated in Figure Q1(b). Given \( \mathrm{R}_{1}=0.5 \Omega, \mathrm{R}_{2}=2 \Omega, \mathrm{L}_{1}=4 \mathrm{mH}, \mathrm{L}_{2}=2 \mathrm{mH}, \mathrm{C}_{1}=1600 \mu \mathrm{F}, \mathrm{C}_{2}=1000 \) \( \mu \mathrm{F} \). (i) Find the impedance at each load. (3 marks) (ii) Find the current at each load and the total current (4 marks) (iii) Compute the complex power at each load. (3 marks) (iv) Determine the total real power and reactive power of the system. (2 marks) (v) Prove the total complex power in \( \mathbf{Q 1}(\mathbf{b}) \) (iv) based on the voltage supply and the total current. (2 marks) (vi) Draw the phasor diagram and the power triangle of the system and calculate the power factor. (5 marks)