Question

A wire of resistance $6\Omega$ is cut into three equal pieces, which are joined to form a triangle. The equivalent resistance between any two corners of the triangle is:

• A. $2\Omega$
• B. $\frac{3}{4}\Omega$
• C. $4\Omega$
• D. $\frac{4}{3}\Omega$

Answer 1

The correct option is D

$\frac{4}{3}\Omega$

The resistance is cut into 3 equal pieces and hence the resistance of each piece is the same. Consider the equivalent resistance across BC(fig).
Here, $R_{AB}$ and $R_{AC}$ are in series and
$R_{eq}=R_{AB}+R_{AC}=2\Omega +2\Omega =4\Omega$
Now, this $4\Omega$ will be parallel to $R_{BC}=2\Omega$
$\frac{1}{R_{eq}}=\frac{1}{4}+\frac{1}{2}=\frac{1+2}{4}=\frac{3}{4}$
$R_{eq}=\frac{4}{3}\Omega$