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. Which of the following graphs will give the values of emf \( \varepsilon \) and internal resistance \( r \)?
Show Hint
Always remember: \(V = \varepsilon - Ir\) gives a straight line with negative slope. Intercept = emf and slope = internal resistance.
Step 1: Write relation between terminal voltage and current.
For a cell:
\[
V = \varepsilon - Ir
\] Step 2: Identify nature of graph.
This equation represents a straight line between \(V\) and \(I\) with:
- Intercept = \(\varepsilon\)
- Slope = \(-r\) Step 3: Analyze slope.
The slope is negative, which means the graph must be a straight line decreasing with increase in current. Step 4: Identify intercept.
When \(I = 0\):
\[
V = \varepsilon
\]
So, the graph must cut the voltage axis at \(\varepsilon\). Step 5: Match with given graphs.
Only graph \(1\) shows a straight line decreasing with current and intercept equal to \(\varepsilon\). Step 6: Interpretation.
The intercept gives emf and the slope gives internal resistance. Step 7: Final answer.
\[
\boxed{1}
\]
