A star$-$connected load with the following parameters is connected to a three$-$phase system:

R$1$ has a resistance of $10$ ohms,

Z$2$ has an impedance of $8$ ohms with a phase angle of $20,$

Z$3$ has an impedance of $8$ ohms with a phase angle of $-30.$

The line$-$to$-$line voltage is $400$ V$.$

a$)$ Provide the phase voltages in terms of magnitude and phase $($use the standard phases as discussed in the lecture$).$

b$)$ Determine the neutral point voltage in terms of magnitude and phase.

c$)$ Calculate the current through conductor $2$ in terms of magnitude and phase.

d$)$ Determine the active power dissipated by impedance Z$2.$