A student investigates resistors connected in parallel using a number of resistors - Edexcel - GCSE Physics - Question 8 - 2020 - Paper 1

The potential difference across the 15 Ω resistor is calculated using Ohm's Law. Since both resistors are in parallel and share the same voltage drop, the potential difference is equal to the voltage supplied by the power source, which can be determined from the circuit.

From the graph in Figure 20, we can analyze the data points to determine that the overall resistance decreases as the number of resistors in parallel increases. Specifically, at approximately three resistors, the graph shows a significant decrease in overall resistance, indicating an inversely proportional relationship.

As more resistors are added in parallel to R, the overall resistance decreases. This trend is not linear; rather, it decreases at a decreasing rate, indicating that each additional resistor contributes less to the overall reduction in resistance. For example, the overall resistance with 1 and 2 resistors shows a notable drop, but the drop becomes less significant with more resistors.

Using Ohm's law, the potential difference (V) across the 15 Ω resistor can be calculated as follows:

$V = I imes R = 0.20 imes 15 = 3 ext{ V}$.

To find the total power (P) dissipated, use the equation:

$P = I^2 imes R$

First, calculate the equivalent resistance (R) of the two resistors in parallel:

rac{1}{R} = rac{1}{15} + rac{1}{20}

Finding R gives:

R = rac{1}{rac{1}{15} + rac{1}{20}} = 8.57 ext{ Ω}

Then, apply the current:

$P = (0.20)^2 imes 8.57 ext{ Ω} = 0.4 ext{ W}$.