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  4. A cell of emf E has an internal resistance r and is connected to a rheostat. When resistance R of rheostat is changed, correct graph of potential difference across it is

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Q. A cell of emf $E$ has an internal resistance $r$ and is connected to a rheostat. When resistance $R$ of rheostat is changed, correct graph of potential difference across it is

Current Electricity

Solution:

$V=I R=\frac{E R}{R+r} \Rightarrow V=\frac{E}{1+r / R}$
image
So as $R$ increases, $V$ also increases. Also at $R=0, V=0$.
But maximum value of $V$ can be $E$ for $R=\infty$
so the graph can be as drawn below.
image