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 $A B$.
Now $CO$ and $OD$ will be in series hence its total resistance $=2\, \Omega$
It is in parallel with $C D$ so equivalent resistance
$=\frac{2 \times 1}{2+1}=\frac{2}{3} \Omega$
This equivalent resistance is in series with $A C$ and $DB$ So total resistance $=\frac{2}{3}+1+1=\frac{8}{3} \Omega$
Now $\frac{8}{3} \Omega$ is parallel to $A B$ that is $2 \,\Omega$ so total resistance
$=\frac{(8 / 3) \times 2}{(8 / 3)+2}=\frac{16 / 3}{14 / 3}=\frac{16}{14}=\frac{8}{7} \Omega$