A student measures the terminal potential difference `(V)` of a cell (of emf `epsilon` and internal resistance `r`) as a function of the current `(I)` flowing through it. The slope and intercept of the graph between `V` and `I`, then respectively, equal

Options

A. `epsilon` and `-r`
B. `-r` and `epsilon`
C. `r` and `- epsilon`
D. `- epsilon` and `r`

Explanation

To solve the problem, we need to analyze the relationship between the terminal potential difference \( V \) and the current \( I \) flowing through a cell with emf \( \epsilon \) and internal resistance \( r \).

### Step-by-Step Solution:

1. **Write the equation for terminal potential difference**:
The terminal potential difference \( V \) of a cell can be expressed as:
\[ V = \epsilon - I \cdot r \]
where \( \epsilon \) is the electromotive force (emf) of the cell, \( I \) is the current, and \( r \) is the internal resistance.

2. **Identify the form of the equation**:
The equation \( V = \epsilon - I \cdot r \) can be rearranged to fit the linear equation format \( y = mx + c \):
\[ V = -r \cdot I + \epsilon \]
Here, \( V \) is the dependent variable (y), \( I \) is the independent variable (x), \( -r \) is the slope (m), and \( \epsilon \) is the y-intercept (c).

3. **Determine the slope**:
From the equation \( V = -r \cdot I + \epsilon \), we can see that the slope \( m \) is:
\[ \text{slope} = -r \]

4. **Determine the y-intercept**:
The y-intercept \( c \) can be identified as the value of \( V \) when \( I = 0 \):
\[ \text{intercept} = \epsilon \]

5. **Conclusion**:
Therefore, the slope and intercept of the graph between \( V \) and \( I \) are:
- Slope: \( -r \)
- Intercept: \( \epsilon \)

### Final Answer:
- Slope: \( -r \)
- Intercept: \( \epsilon \)