In an experiment, a student in the laboratory measures the terminal potential difference (V) of a cell (emf E and internal resistance r) as a function of current I flowing through it and plots a graph taking V on y-axis and I on x-axis. What is the slope of the graph between V and I?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( -r \)
When a cell supplies a current \( I \), its terminal potential difference is less than its emf by the drop across the internal resistance.
\( V = E - I\,r \)
Compare this with the straight line \( y = c + m x \), with \( V \) on the y-axis and \( I \) on the x-axis:
\( \text{intercept } c = E \)
\( \text{slope } m = -r \)
NCERT (2026-27):
Cells, Emf, Internal Resistance – “… If however R is finite, I is not zero. In that case the potential difference between P and N is
\( \displaystyle V = V_{+} + V_{-} - I\,r \)
\( \displaystyle = \varepsilon - I\,r \qquad (3.38) \)
Note the negative sign in the expression (I r) for the potential difference between A and B. This is because the current I flows from B to A in the electrolyte.”