Question

In the network of resistors shown in the figure, the equivalent resistance between $\text{A}$ and $\text{B}$ is

• A. $54\Omega$
• B. $18\Omega$
• C. $36\Omega$
• D. $9\Omega$

Answer 1

The correct option is D $9\Omega$

Since, upper and lower branches are in series, so the network can be redrawn as follows


And each group have parallel combination, so effective resistance of each group is
$R=\frac{6}{2}=3\Omega$


Now the three resistances are in series.

So, equivalent resistance will be

$R_{eq}=3+3+3=9\Omega$

Hence, option $\left(d\right)$ is correct.

Key concept: Circuit can be simplified by successive reduction of series and parallel combination.