Question

A 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

• A. Graph (a): Shows V starting at E when R=0 and decreasing.
• B. Graph (b): Shows V starting at 0 when R=0, increasing as R increases, and asymptotically approaching E.
• C. Graph (c): Shows V starting at 0, increasing to a maximum, and then decreasing back to 0.
• D. Graph (d): Shows V starting at 0 and increasing linearly with R.

Answer 1

Answer: (B)

b

Answer 2

The potential difference V across the external resistance R is given by $V = \frac{ER}{R+r}$, where E is the EMF and r is the internal resistance.

1. When $R=0$, $V=0$.
2. As $R \to \infty$, $V \to E$.
3. The derivative $\frac{dV}{dR} = \frac{Er}{(R+r)^2}$ is always positive, meaning V always increases with R.
4. As R increases, $\frac{dV}{dR}$ decreases, indicating the curve flattens out as it approaches E.

Graph (b) satisfies all these conditions.