Variation of resistance with cell constant is given in which of these graphs?

Options

A.
B.
C.
D.

Answer

To determine the variation of resistance with cell constant, we can follow these steps:

### Step 1: Understand the relationship between resistance and cell constant
The resistance \( R \) of a conductor is given by the formula:
\[ R = \frac{\rho L}{A} \]
where:
- \( R \) is the resistance,
- \( \rho \) is the resistivity of the material,
- \( L \) is the length of the conductor,
- \( A \) is the cross-sectional area of the conductor.

### Step 2: Define the cell constant
The cell constant \( k \) is defined as:
\[ k = \frac{L}{A} \]
Thus, we can rewrite the resistance in terms of the cell constant:
\[ R = \rho k \]

### Step 3: Analyze the equation
From the equation \( R = \rho k \), we can see that resistance \( R \) is directly proportional to the cell constant \( k \) (which is \( \frac{L}{A} \)). This means that as the cell constant increases, the resistance also increases.

### Step 4: Graphical representation
If we were to plot a graph of resistance \( R \) on the y-axis against the cell constant \( k \) on the x-axis, the relationship would be linear. The slope of the line would be equal to the resistivity \( \rho \).

### Conclusion
The correct graph that represents the variation of resistance with cell constant is a straight line graph, indicating a direct proportionality.

### Final Answer
The correct option is the graph that shows a linear relationship between resistance \( R \) and the cell constant \( k \) (or \( \frac{L}{A} \)).

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