To verify Ohm's law, a student connects the voltmeter across the battery as shown in the figure. The measured voltage is plotted as a function of the current, and the following graph is obtained.

If V$$_0$$ is almost zero, identify the correct statement:

To find the electromotive force ($$\text{emf}$$, $$E$$) and the internal resistance ($$r$$) of the battery, we use the relationship between terminal potential difference ($$V$$), current ($$I$$), and internal resistance during discharging.

Here is the structured, step-by-step calculation based on the provided circuit and graph.

1. Governing Equation

The terminal voltage $$V$$ measured by the voltmeter across a battery supplying a current $$I$$ is given by the equation:

$$V = E - Ir$$

Rearranging this into the standard slope-intercept form of a straight line ($$y = mx + c$$):

$$V = (-r)I + E$$

• $$y$$-intercept represents the electromotive force ($$E$$).
• Slope of the line represents the negative internal resistance ($$-r$$).
• Correct Statement: The emf of the battery is $$1.5\text{ V}$$ and its internal resistance is $$1.5\ \Omega$$.
• Correct Option: A

2. Finding the Electromotive Force ($$E$$)

From the given graph, when the current in the circuit is zero ($$I = 0$$):

$$V = 1.5\text{ V}$$

Substituting $$I = 0$$ into our governing equation:

$$1.5 = E - (0)r \implies E = 1.5\text{ V}$$

Thus, the emf of the battery is $$1.5\text{ V}$$.

3. Finding the Internal Resistance ($$r$$)

The graph shows that when the terminal potential difference falls to $$V_0 \approx 0\text{ V}$$, the current reaches its maximum value:

$$I = 1000\text{ mA} = 1\text{ A}$$

Substituting $$V = 0$$, $$E = 1.5\text{ V}$$, and $$I = 1\text{ A}$$ into the equation:

$$0 = 1.5 - (1\text{ A}) \cdot r$$

$$1 \cdot r = 1.5$$

$$r = 1.5\ \Omega$$

Thus, the internal resistance of the battery is $$1.5\ \Omega$$.

Final Conclusion