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Q.
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
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}{2 r}+\frac{1}{2 r}=\frac{2}{2 r}=\frac{1}{r} $
$R=r$
It will in parallel with outer resistance
$\frac{1}{R_{e q}}=\frac{1}{r}+\frac{1}{r}=\frac{2}{r} $
$R_{e q}=\frac{r}{2}$
