A 100 W heater is connected to a 240 V mains supply. Calculate the current drawn and the resistance of the heater.

Given $P = 100\, \text{W}$ and $V = 240\, \text{V}$.

$$I = \frac{P}{V}$$ $$I = \frac{100\, \text{W}}{240\, \text{V}}$$ $$I = \frac{10}{24}\, \text{A}$$ $$I = \frac{5}{12}\, \text{A}$$ $$I \approx 0.41666...\, \text{A}$$ $$\boxed{I \approx 0.42\, \text{A}}$$

Using $V = 240\, \text{V}$ and $I = \frac{5}{12}\, \text{A}$ (from part i):

$$R = \frac{240\, \text{V}}{\frac{5}{12}\, \text{A}}$$ $$R = 240 \times \frac{12}{5}\, \Omega$$ $$R = 48 \times 12\, \Omega$$ $$R = 576\, \Omega$$

Alternatively, using $P = \frac{V^2}{R}$:

$$R = \frac{V^2}{P}$$ $$R = \frac{(240\, \text{V})^2}{100\, \text{W}}$$ $$R = \frac{57600\, \text{V}^2}{100\, \text{W}}$$ $$R = 576\, \Omega$$ $$\boxed{R = 576\, \Omega}$$