A) \[2\]
B) \[\frac{1}{2}\]
C) \[\frac{1}{5}\]
D) \[1\]
Correct Answer: D
Solution :
[d] Given : Number of cells, n = 5, emf of each cell=E Internal resistance of each cell = r In series, current through resistance R \[I=\frac{nE}{nr+R}=\frac{5E}{5r+R}\] In parallel, current through resistance R \[\,I'=\frac{nE}{\frac{r}{n}+R}=\frac{nE}{r+nR}=\frac{5E}{r+5R}\] According to question, \[I=I'\] \[\therefore \frac{5E}{5r+5R}=\frac{5E}{r+5R}\,\Rightarrow 5r+R=r+5R\] \[\text{or }R=r\text{ }\therefore \frac{R}{r}=1\]
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