8. A student investigated how the total resistance of identical resistors connected in parallel varied with the number of resistors.
The student used an ohmmeter to measure the total resistance of the resistors.
Figure 11 shows the student’s circuit with 3 resistors.
The student repeated each reading of resistance three times.
Table 1 shows some of the results for 3 resistors in parallel.
i- Calculate value X in Table 1.
[2 marks]
SOLUTION
ii- The student thought that taking a fourth reading would improve the precision of the results.
The fourth reading was 16.2 Ω.
Explain why the student was wrong.
[2 marks]
ANSWER
The fourth result is less precise because it is less closer to the mean value than other readings.
Figure 12 shows the results box from the investigation.
iii- The student concluded that the number of resistors in parallel was inversely proportional to the mean total resistance.
Explain why the student was correct.
Use data from Figure 12 in your answer.
[3 marks]
ANSWER
We will multiply mean total resistance and number of resistors in parallel for two separate points, if their answers comes the same it can be concluded that there exist an inverse proportionality between number of resitors in parallel and mean total resistance.
So, the two separate points from the graph are
(2, 24)
And (3, 16)
Now, since the product of number of resitors in parallel and mean total resistance at any point on the graph is a constant value, the student’s consclusion stands correct.
iv- Explain why adding resistors in parallel decreases the total resistance.
[2 marks]
ANSWER
There are multiple paths for the electron flow as a result there is a greater current flowing across the circuit at the same potential difference.
