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GCSE Standard Questions: Electric Circuits

Q10. Buffy investigated how the total resistance of identical resistors connected in parallel varied with the number of resistors.

She used an ohmmeter to measure the total resistance of the resistors.

The diagram shows the Buffy's circuit with three resistors.

She repeated each reading of resistance three times.

The table shows some of the results for three resistors in parallel.

Number of resistors
Total resistance in ohms
Reading 1
Reading 2
Reading 3
Mean
3
15.8
15.3
X
15.7

 

(a) Calculate value X

15.8 + 15.3 + X = (3 x 15.7)

X = 47.1 - 31.1

X = 16.0

[2 marks]

(b) Buffy thought that taking a fourth reading would improve the precision of the results.

The fourth reading was 16.2 Ω.

Explain why she was wrong.

Precise results show little variation from each other. Her 4th result was further away from the mean than the other values, and has now resulted in overall less precision as the range of values has increased.

[2 marks]

(c) The graph shows the results box from the investigation.

Buffy concluded that the number of resistors in parallel was inversely proportional to the mean total resistance.

Use data from the graph to explain why she was correct.

If the results were inversely proportional the product of the values for each point will be constant.

You could take any two pairs of values of n and R and showing that n × R = constant for one extra mark

But a third pair of values of n and R showing that n × R = constant would indicate that n × R = constant more strongly.... but even better - do all the points....

2 × 24 = 48,

3 × 16 = 48

4 × 12 = 48,

5 × 9.5 = 47.5 (the only anomoly)

6 × 8 =48

[3 marks]

(d) Explain why adding resistors in parallel decreases the total resistance.

A parallel arrangement allows multiple paths for the current (charge/electrons) to flow down when a potential difference is applied. Therefore the total current increases for the same potential difference as more resistors are added in parallel.

[2 marks]

(Total 9 marks)