In a potentiometer arrangement, a cell gives a balancing point at $75\, cm$ length of wire. This cell is now replaced by another cell of unknown emf. If the ratio of the emf's of two cells respectively is $3: 2$, the difference in the balancing length of the potentiometer wire in above two cases will be.........$cm .$
JEE MAIN 2022, Medium
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$\frac{\varepsilon_{1}}{\varepsilon_{2}}=\frac{\ell_{1}}{\ell_{2}}$
$\frac{3}{2}=\frac{75 \,cm }{\ell_{2}}$
$\ell_{2}=50\, cm$
$\ell_{1}-\ell_{2}=75-50$
$=25 \,cm$
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