Question

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

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

Answer 1

Answer: (A)

$1\Omega$

A balanced wheat stone bridge consists of the resistors such that the ratio of the resistances in the two arms is equal to the resistances in other two arms.

The balanced Wheatstone is represented by:

$\frac{P}{Q}=\frac{R}{S^{\prime }}$

So, the value of $S^{\prime }$ is:

$S^{\prime }=\frac{R\times Q}{P}$

$S^{\prime }=\frac{2\times 2}{2}$

$\Rightarrow S^{\prime }=2\Omega$

Now, since $S^{\prime }$ is the parallel combination of $S$ and a shunt resistance $r$.

So, the value of shunt resistance will be:

$\frac{1}{S^{\prime }}=\frac{1}{S}+\frac{1}{r}$

$\frac{1}{2}=\frac{1}{3}+\frac{1}{r}$

$\therefore r=6\Omega$