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A student measures the terminal potential difference (V) of a cell (of emf $\varepsilon$ and internal resistance $r$ ) as a function of the current (I) flowing through it. The slope and intercept of the graph between $V$ and $I$, then respectively, equal
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The correct answer is:
$-\mathrm{r}$ and $\varepsilon$
According to Ohm's law
$$
\frac{\mathrm{dV}}{\mathrm{dI}}=-\mathrm{r}
$$
and $V=\varepsilon$ if $I=0$
[As $\mathrm{V}+\mathrm{Ir}=\varepsilon$ ]
$\therefore$ Slope of the graph $=-r$ and intercept $=\varepsilon$
$$
\frac{\mathrm{dV}}{\mathrm{dI}}=-\mathrm{r}
$$
and $V=\varepsilon$ if $I=0$
[As $\mathrm{V}+\mathrm{Ir}=\varepsilon$ ]
$\therefore$ Slope of the graph $=-r$ and intercept $=\varepsilon$
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