A cell can be balanced against 110 cm and 100 cm of potentiometer

A cell can be balanced against 110 cm and 100 cm of potentiometer wire, respectively with and without being short circuited through a resistance of 10Ω. Its internal resistance is

Here

E >	ER
	R + r

hence the lengths 110 cm and 100 cm are interchanged.
Without being short-circuited through R, only the battery E is balanced.

E =	V	× l₁ =	V	× 110 ................(i)
	L		L

When R is connected across E, Ri =	V	× l₂
	L

Or, R		E		=	V	× 100..............(ii)
		R + r			L

Dividing (i) by (ii), we get

	R + r	=	110
	R		100

or, 100 R + 100 r = 110 R