Question

Circuit for the measurement of resistance by potentiometer is shown. The galvanometer is first connected at point A and zero-deflection is observed at length PJ = 10 cm. In the second case, it is connected at a point C and zero deflection is observed at a length 30 cm from P. Then what is the unknown resistance X ? 

(A) (R/2) 

(B) (R/3) 

(C) 2R 

(D) 3R

Answer 1

The correct option is (C) 2R.

Explanation:

Let potential gradient along PQ is K then

V_BA = Kℓ₁ = K × 10 = 10K…….as (PJ = 10cm) 

V_BC = Kℓ₂ = K × 30 = 30K…….as (PJ = 30cm) 

∴ (V_BA / V_BC) = (10 / 30) = (1/3) and 

(V_BA / V_BC) = [R / (R + X)] 

∴ [R / (R + X)] = (1/3) 

Hence 3R = R + X i.e. X = 2R