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If n resistors, each of resistance r ohms, are connected in parallel, the equivalent resistance is R. What would be the equivalent resistance if they were connected in series?
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Step-by-step solution
3 stepsDetermine the relationship between , , and for the parallel connection.
When resistors, each of resistance , are connected in parallel, the equivalent resistance is given by the formula:
From this equation, we can express in terms of and :
Calculate the equivalent resistance if the resistors were connected in series.
If the same resistors, each of resistance , were connected in series, the equivalent resistance would be:
Substitute the value of from Step 1 into the series resistance formula.
Substitute into the equation for :
The equivalent resistance of the combination if connected in series would be .
Comparing this with the given options:
[A]
[B]
[C]
[D]The calculated resistance matches option [A].
The final answer is .
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