Question

Six wires, each of resistance $r$, connected so as to form a tetrahedron. The equivalent resistance of the combination when current enters through one corner and leaves through some other corner is

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

Answer 1

Answer: (D)

$\frac{r}{2}$

From the equivalent structure of the tetrahedral, the resistance between point 1 and 2 is

$R_{12}=\frac{(1+1)(1+1)}{(1+1)+(1+1)}r||r$

$\Rightarrow R_{12}=\frac{r\times r}{r+r}$

$\therefore$ req.$\frac{r}{2}$