Current Electricity Charging Discharging Of Capacitors Question 720
Question: 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 $ ( \frac{R}{r} ) $ is
Options:
A) $ 2 $
B) $ \frac{1}{2} $
C) $ \frac{1}{5} $
D) $ 1 $
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Answer:
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 $
BETA
