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