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Question

A battery of emf $$E$$ and internal resistance $$r$$ is connected across a resistance $$R$$. Resistance $$R$$ can be adjusted to any value greater than or equal to zero. A graph is plotted between the current $$(i)$$ passing through the resistance and potential difference $$(V)$$ across it. Select the correct alternative(s).
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A
internal resistance of battery is 5 Ω
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B
emf of the battery is 20V
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C
maximum current which can be taken from the battery is 4A
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D
Vi graph can never be straight line as shown in the figure
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Solution

The correct option is A internal resistance of battery is $$5\space\Omega$$
Some devices having negative resistance show the inverse variation between voltage and current as shown in given figure(in problem).
The terminal voltage of the battery is given by
$$V = E - Ir$$.............................................................(1)
where, $$r$$ is the internal resistance of battery.
when $$I = 0, V = E$$. Hence, $$E = 10$$V.
Now, from graph, if  $$V = 5$$V, $$I = 1$$A, therefore
$$5 = 10 - (1)r$$...................................................from(1)
$$r = 5 \Omega$$
The 
maximum current which can be taken from the battery is
$$I = \dfrac{E}{r} = \dfrac{10}{5} = 2A$$

Physics

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