A potentiometer circuit is set up with an ideal driver cell of emf V₀ (having zero internal resistance) connected directly across a uniform potentiometer wire of length 100 cm and resistance 10 . A given primary cell of emf E is balanced at a length of 60 cm from the positive end. If the potentiometer wire is replaced by another uniform wire of the same length but having a resistance of 20 (keeping the driver cell un

Step-by-step solution

For a potentiometer, the potential gradient k is the potential difference per unit length of the wire. Since the driver cell is ideal (zero internal resistance) and is connected directly across the potentiometer wire, the potential difference across the entire wire is always equal to the emf of the driver cell, V₀ , regardless of the wire's resistance. The potential gradient in the first case is: k₁ = V₀ 100 V/cm The balancing length l₁ for the primary cell of emf E is: E = k₁ l₁ = ( V₀ 100 ) 60 When the wire is re