Question

A uniform metallic wire of resistance $18\Omega$ is bent to form equilateral triangle as shown in figure. Find the equivalent resistance of the resulting connection

• A. $8\Omega$
• B. $12\Omega$
• C. $4\Omega$
• D. $2\Omega$

Answer 1

The correct option is C

$4\Omega$

Explanation for the correct option:

Solving for Equivalent resistance

Since it is an equilateral triangle, $R_1=R_2=R_3=6\Omega$

The circuit can be redrawn as :

As the $2$ resistances are in series the equivalent for them is $R_s=6+6=12\Omega$

The equivalent resistance is,$\frac{1}{R_{eq}}=\frac{1}{12}+\frac{1}{6}$

$R_{eq}=\frac{12}{1+2}=\frac{12}{3}=4\Omega$

Hence, option C is correct.