Question

Find the equivalent resistance between $A$ and $B$.

• A. $\frac{2r}{5}$
• B. $\frac{2r}{7}$
• C. $\frac{8r}{5}$
• D. $\frac{8r}{7}$

Answer 1

The correct option is D $\frac{8r}{7}$

Resistance between $A$ and $B$ can be divided into two equal resistance having value $r/2$. We can observe that the circuit is symmetrical about the line $DF$ and this is perpendicular to $AB$.

So, due to the perpendicular axis symmetry, point $D$ and $F$ are equipotential. These two points can be joined. The circuit can be redrawn as:

Resistance between $C$ and $D$ are in parallel. Their equivalent resistance is
$\frac{r\times r/2}{r+r/2}=\frac{r}{3}$.

Resistances $(AC$ and $CD)$ and $(DE$ and $EB)$ are in series. Their equivalent resistance is
$r+r/3=\frac{4r}{3}$.

Now both the resistance between $(A$ and $D)$ and $(D$ and $B)$ are in parallel. Their equivalent resistance is
$\frac{r\times 4r/3}{r+4r/3}=4r/7$.

Both the resistances are in series. Their eequivalent is,
$R_{AB}=\frac{4r}{7}+\frac{4r}{7}=\frac{8r}{7}$