question_answer

Two sources of equal emf are connected to an external resistance R. The internal resistances of the two sources are \[{{R}_{1}}\] and \[{{R}_{2}}\,({{R}_{2}}>{{R}_{1}})\]. If the potential difference across the source having internal resistance \[{{R}_{2}}\] is zero, then [AIEEE 2005]

A)             \[R={{R}_{1}}{{R}_{2}}/({{R}_{1}}+{{R}_{2}})\]                        

B)                     \[R={{R}_{1}}{{R}_{2}}/({{R}_{2}}-{{R}_{1}})\]                 

C)             \[R={{R}_{2}}\times ({{R}_{1}}+{{R}_{2}})/({{R}_{2}}-{{R}_{1}})\]

D)             \[R={{R}_{2}}-{{R}_{1}}\]

Correct Answer: D

Solution :

            \[i=\frac{2E}{R+{{R}_{1}}+{{R}_{2}}}\] From cell (2)  \[E=V+i{{R}_{2}}=0+i{{R}_{2}}\] Þ \[E=\frac{2E}{R+{{R}_{1}}+{{R}_{2}}}\times {{R}_{2}}\]  Þ \[R={{R}_{2}}-{{R}_{1}}\]