Question

In the network shown in figure each resistance is $1\Omega .$ The effective resistance between $A$ and $B$ is

• A. $\frac{4}{3}\Omega$
• B. $\frac{3}{2}\Omega$
• C. $7\Omega$
• D. $\frac{8}{7}\Omega$

Answer 1

Answer: (D)

By symmetry, currents $i_1$ and $i_2$ from $A$ is the same as $i_1$ and $i_2$ reaching $B$.
As the same current is flowing from $A$ to $O$ and $O$ to $B,O$ can be treated as detached from $AB$.
Now $CO$ and $OD$ will be in series hence its total resistance $=2\Omega$
It is in parallel with $CD$ so equivalent resistance
$=\frac{2\times 1}{2+1}=\frac{2}{3}\Omega$
This equivalent resistance is in series with $AC$ and $DB$ So total resistance $=\frac{2}{3}+1+1=\frac{8}{3}\Omega$
Now $\frac{8}{3}\Omega$ is parallel to $AB$ that is $2\Omega$ so total resistance
$=\frac{(8/3)\times 2}{(8/3)+2}=\frac{16/3}{14/3}=\frac{16}{14}=\frac{8}{7}\Omega$