Question

We have a tetrahedron in which five edges are perfect 1-ohm resistors, but the sixth edge is an unknown resistor R.
Find the equivalent resistance between any two vertices. Prove that we need only two resistance measurements to determine the value of R

Answer 1

Solution

The diagram can be shown as below



Firstly see loop 1432 behave as wheat stone bridge so it's resistance is found

1 $\Omega$ therefore so equivalent resistance at two vertices 1 and 2 is given by

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

We clearly see in above figure above shape is like as Wheatstone brige combination which gives us A resistance value and also in other as also have a resistance it's means we required only two resistances to measure value of R.