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. `epsi" and " -r`
B. `-r " and "epsi`
C. `r " and " -epsi`
D. `-epsi" and " r`

Answer

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

### Step-by-Step Solution:

1. **Understand the Relationship**: According to the problem, we have a cell with an electromotive force \( \epsilon \) and internal resistance \( r \). The terminal potential difference \( V \) can be expressed in terms of \( \epsilon \), \( r \), and \( I \).

2. **Apply Kirchhoff's Voltage Law (KVL)**: We can write the equation for the terminal potential difference as:
\[ V = \epsilon - I \cdot r \]
This equation states that the terminal voltage \( V \) is equal to the emf \( \epsilon \) minus the voltage drop across the internal resistance \( r \) due to the current \( I \).

3. **Identify the Form of the Equation**: The equation \( V = \epsilon - I \cdot r \) can be rearranged to match the linear equation format \( y = mx + c \), where:
- \( y \) is \( V \)
- \( m \) is the slope (which is \(-r\))
- \( x \) is \( I \)
- \( c \) is the y-intercept (which is \( \epsilon \))

4. **Determine the Slope**: From the equation \( V = \epsilon - I \cdot r \), we can see that the slope \( m \) is:
\[ m = -r \]

5. **Determine the Intercept**: The y-intercept \( c \) from the equation is:
\[ c = \epsilon \]

### Final Result:
- The slope of the graph between \( V \) and \( I \) is \( -r \).
- The intercept of the graph is \( \epsilon \).

### Conclusion:
The slope and intercept of the graph between \( V \) and \( I \) are respectively:
- **Slope**: \( -r \)
- **Intercept**: \( \epsilon \)