A nichrome wire AB is made of three parts, AC,CD and DB of resistances in the ratio of 1:2:3. The wire is connected to a battery: If V_1,V_2 and V_3 are the potential drops across AC,CD and DB, respectively, then which of the following is correct?

The problem involves analyzing the potential drops across different sections of the nichrome wire, which 

have resistances in the ratio 1 : 2 : 3.

1. For AC:

V₁ = I . R

1. For CD:

V₂ = I . 2R

1. For DB:

V₃ = I . 3R

V₁ : V₂ : V₃ = ( I . R) : ( I . 2R) : (I . 3R)                [V₁  : V₂  : V₃  =  1 : 2 : 3]

          The resistances of sections AC, CD, and DB are in  the ratio 1: 2 : 3.

          Let R_AC = R, R_CD = 2R, and R_DB = 3R.

          Since the wire is connected in series to the battery, the same current I flows through all parts of the wire.

          According to Ohm's law, the potential drop across a section  is given by:

          V = IR

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