Question

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

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

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 $6 \,Ω$ 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 $S=3\,\Omega$