If internal resistance of a cell is proportional to current drawn from the cell. Then the best representation of terminal potential difference of a cell with current drawn from cell will be

Options

A. A)
B. B)
C. C)
D. D)

Answer

To solve the problem, we need to analyze the relationship between the terminal potential difference (V) of a cell and the current (I) drawn from the cell, given that the internal resistance (R) of the cell is proportional to the current drawn.

### Step-by-Step Solution:

1. **Understanding the Relationship**:
- We know that the terminal potential difference (V) of a cell can be expressed using Ohm's law:
\[ V = E - I \cdot R \]
where \(E\) is the electromotive force (emf) of the cell and \(R\) is the internal resistance.

2. **Proportionality of Internal Resistance**:
- According to the problem, the internal resistance \(R\) is proportional to the current \(I\). We can express this as:
\[ R = k \cdot I \]
where \(k\) is a constant of proportionality.

3. **Substituting Internal Resistance**:
- Substituting \(R\) into the equation for terminal potential difference:
\[ V = E - I \cdot (k \cdot I) \]
This simplifies to:
\[ V = E - k \cdot I^2 \]

4. **Analyzing the Equation**:
- The equation \(V = E - k \cdot I^2\) indicates that the terminal potential difference \(V\) decreases as the square of the current \(I\) increases. This suggests a downward-opening parabola when plotted on a graph.

5. **Graphical Representation**:
- The graph of \(V\) versus \(I\) will show that as \(I\) increases, \(V\) decreases, and specifically, it will decrease in a quadratic manner due to the \(I^2\) term.

6. **Identifying the Correct Option**:
- Among the given options, we look for a graph that shows a downward curve, indicating that as the current increases, the terminal potential difference decreases. The correct representation would be a curve that starts at \(E\) (when \(I=0\)) and decreases as \(I\) increases, resembling a parabola opening downwards.

### Conclusion:
The best representation of the terminal potential difference of a cell with the current drawn from the cell is a downward-opening parabola.