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  4. In a meter bridge, the null point is found at a distance of 25 cm from A. If now a resistance of 10 Ω is connected in parallel with S, the null point occurs at mid point of AB. The value of R is :-

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Q. In a meter bridge, the null point is found at a distance of $25 \,cm$ from $A$. If now a resistance of $10\, \Omega$ is connected in parallel with $S$, the null point occurs at mid point of $AB$. The value of $R$ is :-Physics Question Image

Solution:

Case-1
$\frac{ S }{ R }=\frac{75}{25}$ or $\left(\frac{100-\ell}{\ell}\right)$
$\frac{ S \times 10}{( S +10) R }=\frac{50}{50}$
$\frac{ S }{ R }=3$
$S =3 R \,\,\,\ldots(1)$
Case-2
$S \times 10=( S +10) R$
$3 R \times 10=(3 R +10) R$
$30=3 R +10$
$3 R =20$
$R =\frac{20}{3}=6.67 \,ohm$