Question

A student measures the terminal potential difference \(V\) of a cell (emf \(\varepsilon\) and internal resistance \(r\)) as a function of current \(I\) flowing through it, and draws \(V\) versus \(I\) graph. The slope and intercept of the graph respectively are

• A. \(-r, -\varepsilon\)
• B. \(-r, \varepsilon\)
• C. \(r, -\varepsilon\)
• D. \(r, \varepsilon\)

Hint:

In \(V\)-\(I\) graph of a cell, slope always gives \(-r\) and intercept gives emf \(\varepsilon\).

Answer 1

The Correct Option is B

Step 1: Relation between terminal voltage and current.
\[ V = \varepsilon - Ir \]

Step 2: Compare with straight line equation.
General equation of line:
\[ y = mx + c \]
Here, \(V\) is plotted against \(I\), so:
\[ V = (-r)I + \varepsilon \]

Step 3: Identify slope.
Slope of graph is coefficient of \(I\):
\[ \text{slope} = -r \]

Step 4: Identify intercept.
Intercept is value of \(V\) when \(I = 0\):
\[ \text{intercept} = \varepsilon \]

Step 5: Final conclusion.
\[ \boxed{(-r, \varepsilon)} \] Hence, correct answer is option (B).