Question

A wire is in the form of a tetrahedron. The resistance of each edge is $r$. The equivalent resistance between corners 1-2 and 1-3 are respectively

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

Answer 1

The correct option is A $\frac{r}{2},\frac{r}{2}$

The equivalent resistance of loop $1432$ is $r$. (Wheatstone bridge principle)

And the initial resistance between $1$ and $2$ is $r$.

$\therefore$ the circuit is equivalent to

$\therefore$ Equivalent resistance between $1$ and $2$ is

$\frac{1}{\frac{1}{r}+\frac{1}{r}}=\frac{r}{2}$

Similarly, equivalent resistance between $1$ and $3$ is $\frac{r}{2}$