Discussion
In a circuit, sixteen resistances each of 32 Ω are connected in parallel, the equivalent resistance of this circuit is __________.
Answer: B
The equivalent resistance is 2 Ω.
For n equal resistances R in parallel, each branch adds the same conductance 1/R, so the total conductance is n/R and the equivalent resistance is R/n.
\[ R_{eq} = \frac{R}{n} = \frac{32}{16} = 2\ \Omega \]
A parallel combination is always smaller than its smallest branch, which rules out 32 Ω, 16 Ω and 1024 Ω. 32 Ω is a single branch, and the series sum of sixteen 32 Ω resistors would be 512 Ω.
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