A potentiometer wire AB of length L and resistance 12r is connected to a cell D with emf e and internal resistance 3r. Find length AJ wherein the galvanometer as shown in image shows no deflection.

Potential gradient can be expressed as the potential difference per unit length of wire.

Therefore, the potential gradient = (ε/12r + r) × (12r/L)]

= (ε/13r) × (12r/L)

= 12ε/13L

⇒ (12ε/13L )x = ε/2

⇒ x = \(\frac{13L}{24}\)

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