question_answer

A 2\[\Omega \] resistor is connected in series with R\[\Omega \] resistor. This combination is connected across a cell. When the potential difference across 2\[\Omega \] resistor is balanced on potentiometer wire, null point is obtained at a length of 300 cm. When the same procedure is repealed for R\[\Omega \] resistor, null point is obtained at the length of 350cm, value of R is ;

A)  5\[\Omega \]                                   

B)  3.33\[\Omega \]

C)  4.6\[\Omega \]                               

D)  2.33\[\Omega \]

Correct Answer: D

Solution :

                 It is evident from the diagram that between \[{{J}_{1}}\] and \[{{J}_{2}}\]there will be a point J such that when the jockey is made to touch J, there will be no deflection in the galvanometer. As per principle of potentiometer when a constant current is passed through a wire of Uniform cross-section the potential difference   across any portion of wire is directly  proportional to the length. \[E=Kl\] First case, \[\frac{E}{2+R}\times 2=300\,K\] Second Case, \[\frac{E}{2+R}\times R=350K\] \[\therefore \]              \[\frac{R}{2}=\frac{350}{300}\] \[\Rightarrow \]            \[R=2.33G\Omega \]