Question:
A straight wire of resistance $18~\Omega$ is bent in the form of an equilateral triangle. The effective resistance between any two vertices of the triangle is
A straight wire of resistance $18~\Omega$ is bent in the form of an equilateral triangle. The effective resistance between any two vertices of the triangle is
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Model the triangle as resistors in parallel and series between vertices.
Updated On: Mar 18, 2026
- $6~\Omega$
- $3~\Omega$
- $1~\Omega$
- $4~\Omega$
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The Correct Option is D
Solution and Explanation
Each side: $R = 18/3 = 6~\Omega$
Between any two points: one side direct ($6~\Omega$), two sides in series ($12~\Omega$) in parallel.
$R_{eq} = \dfrac{6 \cdot 12}{6 + 12} = \dfrac{72}{18} = 4~\Omega$
Between any two points: one side direct ($6~\Omega$), two sides in series ($12~\Omega$) in parallel.
$R_{eq} = \dfrac{6 \cdot 12}{6 + 12} = \dfrac{72}{18} = 4~\Omega$
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