1 3. 1 If the electrician touches the live wire he will receive an electric shock - AQA - GCSE Physics - Question 13 - 2018 - Paper 1

To determine the minimum diameter, we first need to calculate the cross-sectional area (A). For a power input of 13.8 kW:

1. Convert power to watts:

   $P = 13.8 \text{ kW} = 13.8 \times 1000 = 13800 \text{ W}$.

2. Use the formula for calculating the area:

   $A = \frac{P}{V} = \frac{13800}{230} \approx 60 \text{ A}$.

3. Substitute into the area formula:

   $A = \frac{13800}{60} \approx 230 \text{ mm}^2$.

4. Finally, using the diameter formula:

   $d = \sqrt{\frac{4A}{\pi}} \approx 3.83 \text{ mm}$.

To find the resistance (R), we can use the formula:

$P = IV$ where $P = 13800 \, \text{W}$, $V = 230 \, \text{V}$. From Ohm's Law: $I = \frac{V}{R}$. Substituting, we get: $P = \frac{V^2}{R} \Rightarrow R = \frac{V^2}{P}$

Now plugging in the values: $R = \frac{230^2}{13800} \approx 3.83 \, \Omega$.