Figure 11 shows how the National Grid connects a power station to consumers - AQA - GCSE Physics - Question 8 - 2023 - Paper 1

The correct equation is:

$P = I R$

To calculate the resistance (R), we use the formula:

$P = I^2 R$

Substituting the values:

$1.60 imes 10^9 = (2000)^2 imes R$

Rearranging gives:

$R = \frac{1.60 imes 10^9}{2000^2}$

Calculating:

$R = 400 \\ (\Omega)$

The efficiency can be expressed as:

$\text{efficiency} = \frac{\text{useful energy output}}{\text{total energy input}}$

Using the efficiency and total energy input:

$\text{useful energy output} = \text{efficiency} \times \text{total energy input}$

Substituting the known values:

$\text{useful energy output} = 0.992 \times 34.2$

Calculating gives:

$\text{useful energy output} = 33.9 \\ (GJ)$