Cell having an emf E and internal resistance r is connected across a variable external resistance R. As the resistance R is increased, the plot of potential difference V across R is given by:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3)
The current in the circuit is \( I = E/(R + r) \), and the potential difference across R is the terminal voltage of the cell:
\( \displaystyle V = IR = \frac{ER}{R + r} = \frac{E}{1 + r/R} \)
At \( R = 0 \), \( V = 0 \), so the graph starts from the origin.
As R increases, \( r/R \) falls and V rises, quickly at first and then more slowly.
As \( R \to \infty \), \( r/R \to 0 \) and \( V \to E \). The curve approaches E but never crosses it, so the line \( V = E \) is an asymptote.
This is the rising curve that levels off below the dashed line at E.
Note: A similar question was also asked in CUET (UG) 2023 on 23-06-2023 (Slot 1).