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)

$3\,\Omega$

Answer 2

The situation can be depicted as shown in figure.

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