question_answer

A cell of emf E is connected with an external resistance R, then potential difference across cell is V. The internal resistance of cell will be:

A) \[\frac{(E-V)R}{E}\]                   

B) \[\frac{(E-V)R}{V}\]

C) \[\frac{(V-E)R}{V}\]                  

D) \[\frac{(V-E)R}{E}\]

Correct Answer: B

Solution :

(b) \[\frac{(E-V)R}{V}\] Current drawn from cell, \[l=\frac{E}{R+r}\]                                                                                             …(1) From Ohm's law, \[V=lR\] \[\Rightarrow l=\frac{V}{R}\]                  ….(2) From eqs. (1) and (2), we have             \[\frac{V}{R}=\frac{E}{R+r}\] \[\Rightarrow r=\left( \frac{E-V}{V} \right)R\]