Q124 / 180 · KCET 2010 · Physics

A battery of emf $E$ has an internal resistance r. A variable resistance $R$ is connected to the terminals of the battery. A current $i$ is drawn from the battery. $V$ is the terminal potential difference. If $R$ alone is gradually reduced to zero, which of the following best describes $i$ and $V$ ?

A
i approaches zero, $V$ approaches E
Correct answer
B
$i$ approaches $\frac{E}{r}, V$ approaches zero
C
$\mathrm{i}$ approaches $\frac{\mathrm{E}}{\mathrm{r}}, \mathrm{V}$ approaches $\mathrm{E}$
D
i approaches infinity, $V$ approaches $E$

Solution

Current, $\mathrm{i}=\frac{\mathrm{E}}{\mathrm{R}+\mathrm{r}}$ when $\mathrm{R}$ decreases to $0, \mathrm{i}=\frac{\mathrm{E}}{\mathrm{r}}$ Similarly, potential difference $V=i R$ when $R$ decreases to $0, \mathrm{~V}=0$

Hence, the correct answer is option: 'B'.

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