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

Options

A.
B.
C.
D.

Explanation

To solve the question regarding the variation of resistance \( R \) with frequency \( f \), we can break it down into the following steps:

### Step 1: Understand the Concept of Resistance
Resistance \( R \) is a property of a material that opposes the flow of electric current. It is defined by Ohm's Law, which states that \( R = \frac{V}{I} \), where \( V \) is the voltage across the resistor and \( I \) is the current flowing through it.

**Hint:** Remember that resistance is a property of the material and does not change with frequency.

### Step 2: Analyze Reactance
In alternating current (AC) circuits, we also deal with reactance, which is the opposition to current flow due to inductance and capacitance. The inductive reactance \( X_L \) is given by \( X_L = \omega L = 2\pi f L \), and the capacitive reactance \( X_C \) is given by \( X_C = \frac{1}{\omega C} = \frac{1}{2\pi f C} \).

**Hint:** Reactance varies with frequency, but we are focusing on resistance here.

### Step 3: Determine the Frequency Dependence
It is important to note that while reactance depends on frequency, resistance does not. This means that regardless of the frequency of the AC signal, the resistance \( R \) remains constant.

**Hint:** Think about how materials behave in AC circuits compared to DC circuits.

### Step 4: Conclusion
Since resistance \( R \) does not change with frequency \( f \), the correct variation of resistance with frequency can be represented as a horizontal line on a graph, indicating that it remains constant.

**Hint:** Visualize the graph: a horizontal line means no change in resistance with frequency.

### Final Answer
The correct variation of resistance \( R \) with frequency \( f \) is that it remains constant, represented as a horizontal line on a graph.