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  4. The efficiency of a cell when connected to a resistance R is 60 %. What will be its efficiency if the external resistance is increased to six times.

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Q. The efficiency of a cell when connected to a resistance $R$ is $60\%.$ What will be its efficiency if the external resistance is increased to six times.

NTA AbhyasNTA Abhyas 2020

Solution:

For $I^{st}$ case
efficiency $=$
$\frac{TPD}{EMF}\times 100=\frac{E R / R + r}{E}=\frac{R}{R + r}$
$0.6=\frac{R}{R + r}$
Hence $r=\frac{2}{3}R$
In $2^{nd}$ case
$x=\frac{6 R}{6 R + r}$
Put the value of $r$ and get the answer.