Q$1.$

a$.$ An alternating current flowing through a circuit has a maximum value of $70$ A $.$ The maximum value of the voltage is $120$ V and lagging the applied current by $\backslash (60^\{\backslash$circ$\}\backslash ),$ and both current and voltage waveforms are sinusoidal. By taking current waveform as reference;

i$.$ Plot the current and voltage waveforms in their correct relationship as mentioned above.

ii$.$ Calculate the impedance and draw their impedance triangle.

b$.$ Referring to Figure Q$2($a$)$ and Q$2($b$)$ as given below.

i$.$ Write the expression of $\backslash (\backslash$mathrm$\{$V$\}\_\{1\}(\backslash$mathrm$\{$t$\})\backslash )$ in time$-$domain when $\backslash (\backslash$mathrm$\{$f$\}=60\backslash$mathrm$\{$~Hz$\}\backslash ).$

ii$.$ Determine:

a$)$ Total impedance, Z for the circuit in figure Q $2($a$).$

b$)$ Current $\backslash (\backslash$mathrm$\{$I$\}\_\{\backslash$mathrm$\{$T$\}\},\backslash$mathrm$\{$I$\}\_\{1\}\backslash )$ and $\backslash (\backslash$mathrm$\{$I$\}\_\{2\}\backslash )$ and the voltage across the capacitor, Vc and inductor, $\backslash (\backslash$mathrm$\{$V$\}\_\{\backslash$mathrm$\{$L$\}\}\backslash )$ in both polar and rectangular form.

c$)$ Sketch the phasor diagram of $\backslash (\backslash$mathrm$\{$Vc$\},\backslash$mathrm$\{$V$\}\_\{\backslash$mathrm$\{$L$\}\}\backslash )$ and $\backslash (\backslash$mathrm$\{$V$\}\_\{1\}\backslash ).$

c$.$ A balanced three$-$phase load consists of three coils in which each of them having a resistance of $4\backslash (\backslash$Omega $\backslash )$ and inductance of $20$ mH $.$ The coils are star connected to a $400$ V $,$ three$-$phase $50$ Hz supply system. Determine;

i$.$ Phase voltage and phase current

ii$.$ Line voltage and line current

iii. Draw the phasor diagram for both phase voltage and phase current. Fig. Q$2($a$)$

Fig. $2$Q$($b$)$