Question

Three resistances $P$ , $Q$ , $R$ each of $2\Omega$ and an unknown resistance $S$ form the four arms of a Wheatstone’s bridge circuit. When a resistance of $6\Omega$ is connected in parallel to $S$ the bridge gets balanced. What is the value of $S$ ?

• A. $2\Omega$
• B. $3\Omega$
• C. $6\Omega$
• D. $1\Omega$

Answer 1

Answer: (B)

The bridge formed with given resistances is a balanced Wheatstone’s bridge.
The situation can be depicted as shown in figure.

As resistances $S$ and $6\Omega$ are in parallel their effective resistance is
$\frac{6S}{6+S}\Omega$
As the bridge is balanced, hence it is balanced Wheatstone’s bridge.
For balancing condition,
$\frac{P}{Q}=\frac{R}{\left(\frac{6S}{6+S}\right)}$
or $\frac{2}{2}=\frac{2\left(6+S\right)}{6S}$
or $3S=6+S$
or $S=3\Omega$