question_answer

A uniform metallic wire has a resistance of \[18\,\Omega \] and is bent into an equilateral triangle. Then, the resistance between any two vertices of the triangle is-

A) \[12\,\Omega \]                                   

B) \[2\,\Omega \]

C) \[4\,\Omega \]                           

D)   \[8\,\Omega \]

Correct Answer: C

Solution :

A uniform wire resistance is\[18\,\Omega \]. When it is bended into equilateral triangle then length of each side is same and its resistance is \[\frac{18}{3}\,\,=\,\,6\,\Omega \].   \[{{\operatorname{R}}_{eqAB}}\,=\,\frac{12\times 6}{12+6}\,=\,\frac{72}{18}\,=\,4\,\Omega \]