Question

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

• A. $-r$ and $\varepsilon $
• B. $r$ and $-\varepsilon $
• C. $-\varepsilon$ and $r$
• D. $\varepsilon $ and $-r$

Answer 1

Answer: (A)

Given: A student measures the terminal potential difference $(V)$ of a cell ( of emf $E$ and internal resistance $r$ ) as a function of the current $(I)$ flowing through it.
To find the slope and intercept of the graph between $V$ and I
Solution:
The general equation of $EMF$ in cell:
$V = E - ir $
$\Rightarrow V = E + i (- r )$
Compare it with standard equation of the line:
$y=m x+c $
$\Rightarrow y=c+m x$
Since graph of student is $V$ vs $I$
$\therefore, V$ is $y$ and $I$ is $x$
Therefore, $E$ is intercept and $(-r)$ is slope