If a variable resistance is connected to a cell of constant e.m.f., then which one of the following grphs represnets the relationship between current I and resistanc R?

Options

A.
B.
C.
D.

Explanation

To solve the problem of determining the relationship between current (I) and resistance (R) when a variable resistance is connected to a cell of constant electromotive force (e.m.f.), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Circuit**:
- We have a circuit with a variable resistor (R) connected to a cell with a constant e.m.f. (V). The e.m.f. remains constant regardless of the changes in resistance.

2. **Use Ohm’s Law**:
- According to Ohm’s Law, the relationship between voltage (V), current (I), and resistance (R) is given by the formula:
\[ V = I \times R \]
- Rearranging this formula to express current in terms of resistance gives:
\[ I = \frac{V}{R} \]

3. **Analyze the Relationship**:
- Since V is constant (the e.m.f. of the cell), we can see that current (I) is inversely proportional to resistance (R):
\[ I \propto \frac{1}{R} \]
- This means that as resistance increases, current decreases.

4. **Graphical Representation**:
- To graph this relationship, we plot current (I) on the y-axis and resistance (R) on the x-axis.
- As R increases from 0 to a large value, I will start from a very high value (approaching infinity when R is 0) and decrease towards 0 as R approaches infinity.

5. **Shape of the Graph**:
- The graph will not be a straight line but rather a hyperbolic curve that approaches the axes. Specifically, it will approach the y-axis (current) as R approaches 0 and the x-axis (resistance) as I approaches 0.

6. **Identifying the Correct Option**:
- Based on the above analysis, the correct graph will show a curve that starts from a high value of current when resistance is low and decreases as resistance increases. This corresponds to the fourth option in the provided choices.

### Conclusion:
The graph that represents the relationship between current (I) and resistance (R) when a variable resistance is connected to a cell of constant e.m.f. is a hyperbolic curve, indicating that current is inversely proportional to resistance.