The correct curve between `X_(L)` and `logf` is

Options

A.
B.
C.
D.

Explanation

To find the correct curve between \( X_L \) (inductive reactance) and \( \log f \) (the logarithm of frequency), we start by recalling the relationship between \( X_L \) and frequency \( f \).

### Step-by-Step Solution:

1. **Understand the Relationship**:
The inductive reactance \( X_L \) is given by the formula:
\[ X_L = \omega L \]
where \( \omega \) (angular frequency) is related to frequency \( f \) by:
\[ \omega = 2\pi f \]
Therefore, we can rewrite \( X_L \) as:
\[ X_L = 2\pi f L \]

2. **Express \( X_L \) in terms of \( f \)**:
From the above equation, we can express \( X_L \) as:
\[ X_L = 2\pi L f \]
This indicates a linear relationship between \( X_L \) and \( f \).

3. **Taking the Logarithm of Frequency**:
We want to plot \( X_L \) against \( \log f \). To do this, we can express \( f \) in terms of \( \log f \):
\[ f = e^{\log f} \]

4. **Substituting \( f \) into the Equation**:
Now, substituting \( f = e^{\log f} \) into the equation for \( X_L \):
\[ X_L = 2\pi L e^{\log f} \]
This shows that \( X_L \) is proportional to \( e^{\log f} \).

5. **Understanding the Graph**:
Since \( X_L \) is directly proportional to \( f \), and \( f \) is an exponential function of \( \log f \), the relationship between \( X_L \) and \( \log f \) will be a straight line. Specifically, it will be a linear graph where \( X_L \) increases exponentially as \( \log f \) increases.

6. **Plotting the Graph**:
On the graph, we will plot \( X_L \) on the y-axis and \( \log f \) on the x-axis. The resulting graph will show a linear increase, indicating that as \( \log f \) increases, \( X_L \) also increases.

### Conclusion:
The correct curve between \( X_L \) and \( \log f \) is a straight line with a positive slope.