Question

Find the equivalent resistance between the points $A$ and $B$.

• A. $2\Omega$
• B. $4\Omega$
• C. $8\Omega$
• D. $16\Omega$

Answer 1

Answer: (B)

It is a balanced Wheatstone bridge.
The given circuit can be redrawn as :

The ratio of resistances in the arms are
$\frac{P}{Q}=\frac{4}{8}=\frac{1}{2}$
and $\frac{2}{4}=\frac{1}{2}=\frac{R}{S}$
Hence, $\frac{P}{Q}=\frac{R}{S}=\frac{1}{2}$
Therefore, bridge is balanced, so potential across $C$ and $D$ is same.
Also $4\Omega$ and $8\Omega$ are connected in series and $2\Omega$ and $4\Omega$ are also in series.
Hence, circuit reduces to as shown,

The effective resistance is
$\frac{1}{R^{\prime }}=\frac{1}{12}+\frac{1}{6}=\frac{1+2}{12}=\frac{3}{12}$
$\Rightarrow R^{\prime }=4\Omega$