The length of a potentiometer wire is ℓ . A cell of emf E is balanced at a length ℓ /3 from the positive end of the wire. If the length of the wire is increased by ℓ /2. At what distance will be the s

Question

The length of a potentiometer wire is ℓ . A cell of emf E is balanced at a length ℓ /3 from the positive end of the wire. If the length of the wire is increased by ℓ /2. At what distance will be the same cell give a balance point.

TestHub · Accepted Answer

Potential gradient in the first case = ℓ E 0 ​ ​ ∴ E = ( 3 ℓ ​ ) ⋅ ( ℓ E 0 ​ ​ ) = 3 E 0 ​ ​ Potential gradient in second case = 3 ℓ /2 E 0 ​ ​ (x) 3 ℓ 2 E 0 ​ ​ From equations (i) and (ii), 3 E 0 ​ ​ − ( 3 ℓ 2 E 0 ​ ​ ) x ⇒ x = 2 ℓ ​

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