Q$\mathrm{.}3$ Briefly explain why, in a pure inductor, the current lags the voltage by $90$o in phase. Assume both the voltage and current vary sinusoidally$.(4$ marks$)$ Briefly, explain why gas generation currently plays an important role in the operation of our power system. $(4$ marks$)$ A small office draws $18\mathrm{.}7$ kW from the local supply at a voltage of $230$ V $(50$Hz$)$ and at a lagging power factor of $0\mathrm{.}79.$ If the building$$s energy manager commissions work to improve this power factor to $0\mathrm{.}95$ calculate the following. $($a$)$ The reduction in the magnitude of current drawn from the supply due to power factor correction. $(4$ marks$)($b$)$ The rating of the capacitor bank required $($F$).($c$)$ Briefly describe how power factor correction works. $(4$ marks$)$