Question

The equivalent resistance between points $A$ and $B$ in the network shown in figure is:

• A. $\frac{15}{7}\text{R}$
• B. $\frac{8}{7}\text{R}$
• C. $\frac{12}{7}\text{R}$
• D. $\frac{16}{7}\text{R}$

Answer 1

The correct option is B $\frac{8}{7}\text{R}$

From symmetry of current distribution, the junction becomes irrelevant, so the network can be modified as

From the above circuit,
$R_{AB}=(R+R||2R+R)||2R$
$\Rightarrow R_{AB}=(R+\frac{2R}{3}+R)||2R$
$\Rightarrow R_{AB}=\frac{8R}{3}||2R$
$\Rightarrow R_{AB}=\frac{8}{7}R$