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
$\frac{1}{R'}=\frac{1}{12}+\frac{1}{6}=\frac{1+2}{12}=\frac{3}{12}$
$\Rightarrow R'=4\, \Omega$