Question:
A wire of $25\ \Omega$ resistance is cut into n pieces of equal length. If these pieces are connected in parallel, the equivalent resistance is $1\ \Omega$, then n is:
A wire of $25\ \Omega$ resistance is cut into n pieces of equal length. If these pieces are connected in parallel, the equivalent resistance is $1\ \Omega$, then n is:
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Connecting $n$ pieces of a wire in parallel reduces resistance by a factor of $n^2$.
Updated On: Apr 28, 2026
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The Correct Option is D
Solution and Explanation
Step 1: Concept
Each piece has resistance $r = R/n$.
Step 2: Analysis
In parallel, $R_{eq} = r/n = (R/n)/n = R/n^2$.
Step 3: Calculation
$1 = 25/n^2 \implies n^2 = 25 \implies n = 5$. Final Answer: (D)
Each piece has resistance $r = R/n$.
Step 2: Analysis
In parallel, $R_{eq} = r/n = (R/n)/n = R/n^2$.
Step 3: Calculation
$1 = 25/n^2 \implies n^2 = 25 \implies n = 5$. Final Answer: (D)
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