Question

Six wires, each of resistance $r$, are 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)

Six wires each of resistance $r$ form a tetrahedron as shown in the following figure

The equivalent circuit of this tetrahedron

It is circuit of Wheatstone the equivalent resistance of upper circuit
$\frac{1}{R}=\frac{1}{2r}+\frac{1}{2r}=\frac{2}{2r}=\frac{1}{r}$
$R=r$
It will in parallel with outer resistance
$\frac{1}{R_{eq}}=\frac{1}{r}+\frac{1}{r}=\frac{2}{r}$
$R_{eq}=\frac{r}{2}$