Question

Consider $12$ resistors arranged symmetrically in shape of bipyramid $ABCDEF$. The resistance of each resistor is $R$.

• A. The effective resistance between $E$ and $F$ is $\frac{R}{2}$
• B. The effective resistance between $A$ and $C$ is $2R$
• C. The effective resiztance between $E$ and $F$ is $R$
• D. The effective resiztance between $A$ and $C$ is $\frac{R}{2}$

Answer 1

The correct option is A The effective resistance between $E$ and $F$ is $\frac{R}{2}$

Due to existence of a plane of symmetry passing through points AECF, the potentials at points B and D is same. Hence no current flows in branches AB, BC, CD and DA. The only left resistances are ECF, EBF, EDF and EAF.

Resistance of branch ECF$=R+R=2R$

Resistance of branch EBF$=R+R=2R$

Resistance of branch EDF$=R+R=2R$

Resistance of branch EAF$=R+R=2R$

Since all of them are in parallel combination, the equivalent resistance between E and F becomes $\frac{R}{2}$.