The resistance of the meter bridge $AB$ in given figure is $4\,\Omega $. With a cell of emf $\varepsilon \, = 0.5\,\,V$ and rheostat resistance $R_h = 2\,\Omega $ the null point is obtained at some point $J.$ When the cell is replaced by another one of emf $\varepsilon \, = {\varepsilon _2}$ the same null point $J$ is found for $R_h = 6\,\Omega .$ The $emf$ ${\varepsilon _2}$ is ................. $V$
A$0.4$
B$0.3$
C$0.6$
D$0.5$
JEE MAIN 2019, Diffcult
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B$0.3$
b $0.5=\frac{6}{(2+\lambda L)} \lambda x$ ......$(1)$
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