Question

In Wheatstones network $P=2\Omega ,Q=2\Omega ,R=2\Omega$ and $S=3\Omega$. The resistance with which $S$ is to shunted in order that the bridge may be balanced is

• A. $1\Omega$
• B. $2\Omega$
• C. $4\Omega$
• D. $6\Omega$

Answer 1

The correct option is D $6\Omega$

Let a resistance $r$ is connected in parallel to $S$ so to make an equivalent resistance $S^{\prime }$ for balancing the wheat stone bridge.

A balanced wheat stone bridge must satisfy $\frac{P}{Q}=\frac{R}{S^{\prime }}$

$\therefore$ $\frac{2}{2}=\frac{2}{S^{\prime }}$ $⟹S^{\prime }=2\Omega$

For parallel connection : $S^{\prime }=\frac{rS}{r+S}$

$\therefore$ $2=\frac{r\times 3}{r+3}$

Or $2r+6=3r$ $⟹r=6\Omega$