The combined resistance of n identical resistors connected in parallel is R_n - AQA - A-Level Physics - Question 26 - 2017 - Paper 1
Question 26
The combined resistance of n identical resistors connected in parallel is R_n.
Which statement correctly describes the variation of R_n as n increases?
A R_n decr... show full transcript
Worked Solution & Example Answer:The combined resistance of n identical resistors connected in parallel is R_n - AQA - A-Level Physics - Question 26 - 2017 - Paper 1
Step 1
Identify the Relationship of Resistors in Parallel
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Answer
The combined resistance, R_n, of n identical resistors in parallel can be calculated using the formula:
rac{1}{R_n} = n imes rac{1}{R}
where R is the resistance of a single resistor. This implies that as n (the number of resistors) increases, the overall resistance R_n decreases.
Step 2
Analyze the Variation
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Answer
From the formula, as n increases, R_n gets smaller. The decrease is not linear because the formula indicates that the relationship between R_n and n is inversely proportional. Therefore, R_n decreases non-linearly.
Step 3
Select the Correct Option
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Answer
Based on the analysis, the correct option is B: R_n decreases non-linearly as n increases.
