$2.$ A balanced $3-$phase $\backslash (240-\backslash$mathrm$\{$V$\}50-\backslash$mathrm$\{$Hz$\}\backslash )$ source supplies power to a $3-$phase induction motor, a balanced delta connected load with per$-$phase impedance of $\backslash (50/60^\{\backslash$circ$\}\backslash$Omega $\backslash ),$ and a star$-$connected resistive load with $\backslash (10\backslash$Omega $\backslash )$ perphase impedance. The motor draws a total of $2$ kVA at power factor of $0\mathrm{.}7.$

Sketch a circuit diagram for the entire system of three loads. $(5$ marks$)$

Determine the following parameters:

a$)$ Line current for each load $(12\mathrm{.}5$ marks$)$

b$)$ Phase current for each load $(12\mathrm{.}5$ marks$)$

c$)$ Source line current $(\backslash (\backslash$mathbf$\{10\}\backslash )$ marks$)$

d$)$ Active power taken by each load $(\backslash (\backslash$mathbf$\{12.5\}\backslash )$ marks$)$

e$)$ Reactive power taken by each load $(\backslash (\backslash$mathbf$\{12.5\}\backslash )$ marks$)$

f$)$ Overall power factor of the system $(10$ marks$)$

Design a capacitor bank required to correct the overall power factor to $\backslash (100\backslash \%\backslash ).$ Specify the values of the capacitors and show their connection on the circuit diagram. $(25$ marks$)$