A student investigates how the potential difference across the secondary coil of a transformer changes with the number of turns on the secondary coil - OCR Gateway - GCSE Physics - Question 21 - 2023 - Paper 4

The potential difference across the secondary coil (V_s) can be calculated using the transformer equation:

$\frac{V_s}{V_p} = \frac{N_s}{N_p}$

where:

• V_s = potential difference across the secondary coil
• V_p = potential difference across the primary coil = 230 V
• N_s = number of turns in the secondary coil = 300
• N_p = number of turns in the primary coil = 3540

Rearranging the equation gives:

$V_s = V_p \times \frac{N_s}{N_p}$

Substituting the known values:

$V_s = 230 V \times \frac{300}{3540} \approx 19.5 V$

The current in the primary coil (I_p) can be calculated using the relationship between power and current:

Using the transformer equation again: $P_{primary} = V_p \times I_p = P_{secondary}$

Where:

• Current in secondary coil (I_s) = 4.62 A
• Potential difference across secondary coil (V_s) = 19.5 V (from previous calculation)

So, $P_{secondary} = V_s \times I_s = 19.5 V \times 4.62 A \approx 90.15 W$

Now we set the power in the primary side equal to this value: $90.15 W = 230 V \times I_p$

Rearranging gives: $I_p = \frac{90.15 W}{230 V} \approx 0.392 A$

According to the graph, the relationship between the turns ratio and power loss is not linear. When the turns ratio doubles, the power loss does decrease, but it does not halve proportionally. This indicates that the student's claim does not accurately reflect the data shown in the graph, as power loss decreases at a rate slower than the doubling of the turns ratio.

Step-up transformers are used in the national grid primarily to increase the voltage for efficient power transmission over long distances. Higher voltage reduces current and decreases resistive losses in the transmission lines, leading to more efficient energy transfer. This minimizes energy loss as heat due to resistance, allowing electricity to be transported over vast distances with minimal loss.