The correct variation of resistance `R` with frequency `f` is given by

Options

A.
B.
C.
D.

Explanation

To determine the correct variation of resistance \( R \) with frequency \( f \), we need to analyze the relationship between resistance and frequency in an AC circuit.

### Step-by-Step Solution:

1. **Understanding Resistance**:
- Resistance \( R \) is a property of a material that opposes the flow of electric current. It is defined by Ohm's law as \( R = \frac{V}{I} \), where \( V \) is voltage and \( I \) is current.

2. **Frequency Dependence**:
- In an AC circuit, the impedance \( Z \) can have components that depend on frequency, such as inductive reactance \( X_L \) and capacitive reactance \( X_C \).
- Inductive reactance is given by \( X_L = \omega L = 2\pi f L \), which increases with frequency.
- Capacitive reactance is given by \( X_C = \frac{1}{\omega C} = \frac{1}{2\pi f C} \), which decreases with frequency.

3. **Resistance vs. Reactance**:
- While \( X_L \) and \( X_C \) vary with frequency, the resistance \( R \) itself does not change with frequency. It is a constant value for a given resistor regardless of the frequency of the AC signal.

4. **Graphical Representation**:
- If we were to plot resistance \( R \) against frequency \( f \), the graph would be a horizontal line, indicating that \( R \) remains constant as \( f \) changes.

5. **Conclusion**:
- Therefore, the correct variation of resistance \( R \) with frequency \( f \) is that \( R \) remains constant regardless of the frequency.

### Final Answer:
The correct variation of resistance \( R \) with frequency \( f \) is that \( R \) is constant.