Correct option is (b) 25
Explanation: The current passing through the potentiometer wire:
I = \(\frac {8}{(30 + 20)} = \frac {8}{50}\) = 0.16A
The potential difference across the potentiometer wire:
V = current × resistance = 0.16 × 30 = 4.8V
Length of the wire = 100 cm
k = \(\frac {V}{l} = \frac {4.8}{100}\) = 0.048
The emf 1.2V is balanced against the length L of the wire, i.e. 1.2 = kL
Length = \(\frac {1.2}{k} = \frac {1.2}{0.048}\) = 25 cm
Therefore, the length L is 25 cm.