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. $6~\Omega$
• B. $3~\Omega$
• C. $1~\Omega$
• D. $4~\Omega$

Hint:

Model the triangle as resistors in parallel and series between vertices.

Answer 1

The Correct Option is D

Each side: $R = 18/3 = 6~\Omega$
Between any two points: one side direct ($6~\Omega$), two sides in series ($12~\Omega$) in parallel.
$R_{eq} = \dfrac{6 \cdot 12}{6 + 12} = \dfrac{72}{18} = 4~\Omega$