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Question

A battery of e.m.f E and internal resistance r is connected across a resistance R. The 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 alternatives.

A
Internal resistance of the battery is 5Ω
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B
E.m.f. of the battery is 10 V.
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C
Maximum current which can be taken from the battery is 2 A.
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D
V – I graph can never be a straight line as shown in the figure.
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Solution

The correct option is C Maximum current which can be taken from the battery is 2 A.
The circuit diagram for the given case can be drawn as shown below.
where V is potential across battery, E is emf of the battery, r is internal resistance of the battery and R is external resistance.
The relation between emf and potential across battery is given by
V=EIr(1)
The above relation matches with straight line equation, y=mx+C
where slope, m=r and y-intercept, C=E
Hence option D is incorrect.
From graph, y intercept is 10 V.
Since y-intercept, C=E=10V
Hence option B is correct.
Now slope of the VI graph is m=01020=5
Since slope, m=r
r=5 Ω
Hence option A is correct.
Maximum current can be drawn from the battery when external resistance R is zero.
Thus relation (1) becomes,
0=EIr
E=Ir
I=Er=105=2 A
Hence option C is correct.

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