Question

Twelve resistors each of resistance $r$ are connected together so that each lies along the edge of the cube as shown in the figure. The equivalent resistance between points $1$ and $3$ is

• A. $\frac{1}{4}r$
• B. $\frac{1}{2}r$
• C. $\frac{3}{4}r$
• D. $\frac{5}{4}r$

Answer 1

The correct option is C $\frac{3}{4}r$



From the above diagram, we can see that points $(6,8)$ are symmetrically located with respect to points $1$ and $3$. So they are at same potentials (equipotential point).

Similarly, points $(2,4)$ are also symmetrically located with respect to points $1$ and $3$. So they are again at same potentials.

Considering above point redrawing the circuit.


On simplifying it by using parallel and series combination formula,


Since above diagram is a balanced Wheatstone bridge, so circuit become




Hence, the equivalent resistance between points $1$ and $3$ is $3r/4$.

Therefore, option $\left(c\right)$ is correct.