Task 2: i. Simplify the formula for the current I to its most basic form. ii. Draw a circuit diagram showing how to connect the four batteries in parallel to increase capacity while maintaining 12V. i

The formula is $I = k \times S^m / S^n$.
Given constants are $k=5$, $m=3$, $n=2$.

The simplified formula for current $I$ is $\boxed{I = \text{5S}}$.

Task 2, Part ii:

The formula for inductive reactance is $X_L = 2 \pi f L$.
Given values are $f = 50Hz$, $L = 0.1H$, and $\pi = 3.14$.

The inductive reactance $X_L$ is $\boxed{\text{31.4 \Omega}}$.

Task 2, Part iv:

The formula for capacitive reactance is $X_C = \frac{1}{2 \pi f C}$.
Given values are $f = 50Hz$, $C = 100\mu F$, and $\pi = 3.14$.
Convert capacitance to Farads: $C = 100\mu F = 100 \times 10^{-6} F = 1 \times 10^{-4} F$.

The capacitive reactance $X_C$ is $\boxed{\text{31.85 \Omega}}$.

Task 2, Part v:

The formula for impedance in a series RC circuit is $Z = \sqrt{R^2 + X_C^2}$.
Given values are $R = 10\Omega$ and $X_C = 15\Omega$.

The total impedance $Z$ is $\boxed{\text{18.03 \Omega}}$.