c$)$ Correct cable sizing is important in electrical installations as IET regulations must be complied with. Incorrect cables could lead to a hazard if the current is too large for the chosen cable to cope with. As part of your ongoing development, you decide to investigate circuit calculations and come across the following questions. Have a go at solving them and see what kinds of numbers are involved.

i$)$ The instantaneous current $i$ at time $t$ in a LR series circuit is given by the expression:

$i=\frac{V}{R}(1-e^{\frac{-Rt}{L}})$

A coil connected to $99$ volts DC supply has an inductance of $51$ and a resistance of $8.$ Calculate the current after $0\mathrm{.}05$ s and the time for the current to reach $10$ A $.$

ii$)$ A sinusoidal voltage supply of is connected to an impedance of $61+18$j Ohms. Calculate the current flowing through the circuit.