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NEET2010PhysicsCurrent ElectricityActual

A potentiometer circuit is set up as shown. The potential gradient across the potentiometer wire, is k volt/cm and the ammeter, present in the circuit, reads 1.0 A when two way key is switched off. The balance points, when the key between the terminals (i) 1 and 2 (ii) 1 and 3 , is plugged in, are found to be at lengths l ₁ ~cm and l ₂ ~cm respectively. The magnitudes, of the resistors R and X , in ohm, are then, equ

Options

  1. Ak ( l ₂- l ₁ ) and kl ₂
  2. Bkl ₁ and k ( l ₂- l ₁ )
  3. Ck ( l ₂- l ₁ ) and kl ₁
  4. Dkl ₁ and kl ₂

Correct answer

B. kl ₁ and k ( l ₂- l ₁ )

Step-by-step solution

The balancing length for R (when 1,2 are connected) be is l₁ and balancing length for R + X (when 1,3 is connected is l ₂ ) Then iR = kl ₁ and i ( R + X )= kl ₂ Given i =1 ~A array r R = kl ₁ R + X = kl ₂ array Subtracting Eq. (i) from Eq. (ii), we get X = k ( l ₂- l ₁ )

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