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  4. Five cells each of emf E and internal resistance r send the same amount of current through an external resistance R whether the cells are connected in parallel or in series. Then the ratio ( (R/r) ) is

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Q. Five cells each of emf $E$ and internal resistance $r$ send the same amount of current through an external resistance $R$ whether the cells are connected in parallel or in series. Then the ratio $\left( \frac{R}{r} \right)$ is

KEAMKEAM 2014Current Electricity

Solution:

When $5$ cell are joined in parallel as shown,
$i=\frac{\text { net emf }}{\text { total resistance }}$
image
$i=\frac{5 \,E}{5 \,R+r}$
When $5$ cell are joined in series as shown,
image
$i=\frac{5\, E}{5\, r+R}$
So, according to the questions
$\frac{5 \,E}{5\, R+r}=\frac{5 \,E}{5\, r+R} $
$5\, R+r=5 \,r+R$
$4 \,R=4 \,r \Rightarrow \frac{R}{r}=\frac{4}{4}$
$\frac{R}{r}=1$