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

The Correct Option is 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 $\hspace20mm =\frac{2 \times 1}{2+1} = \frac{2}{3} \Omega$

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 $=\frac{(8/3) \times 2}{(8/3)+2}=\frac{16/3}{14/3}=\frac{16}{14}=\frac{8}{7} \Omega$