A student measures the terminal potential difference $V$ of a cell of $\operatorname{emf} \varepsilon$ and internal resistance $r$ as a function of the current I flowing through it. Which of the following graphs will give the values of emf $\varepsilon$ and internal resistance $r$ ?

The terminal potential difference $V$ of a cell with emf $\varepsilon$ and internal resistance $r$ is given by the equation $V = \varepsilon - Ir$.

This equation represents a linear relationship between $V$ and $I$, which can be written in the form $y = mx + c$ as $V = -rI + \varepsilon$.

Comparing this with the equation of a straight line, the intercept on the $V$-axis (when $I = 0$) is $\varepsilon$, and the slope of the line is $-r$.

Graph 1 shows $V$ on the vertical axis and $I$ on the horizontal axis with a negative slope, which matches the equation $V = -rI + \varepsilon$. The $V$-intercept is $\varepsilon$ and the magnitude of the slope gives the internal resistance $r$.

Answer: $1$