Question

If we increase the frequency of an a.c. supply, then inductive reactance

• A. increases directly with the square of frequency
• B. increases as it is directly proportional to frequency
• C. decreases inversely with the square of frequency
• D. decreases as it is inversely proportional to the frequency

Hint:

Think of an inductor as an elements that opposes changes in current. Higher frequencies mean the current changes direction much faster, forcing the inductor to push back harder. Thus, reactance must scale up linearly with frequency ($X_L \propto f$), unlike capacitive reactance which drops at higher frequencies ($X_C \propto \frac{1}{f}$).

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
We need to determine how the inductive reactance ($X_L$) of an ideal inductor responds when the fundamental frequency ($f$) of the connected alternating current source increases.

Step 2: Key Formula or Approach:
The inductive reactance ($X_L$) represents the opposition that an inductor offers to an alternating current. It is mathematically defined by the formula:
$$X_L = \omega L = 2\pi f L$$ where $\omega$ is the angular frequency, $f$ is the cyclic frequency, and $L$ is the self-inductance of the component.

Step 3: Detailed Explanation:
Let's analyze the mathematical relationship from the inductive reactance equation:
$$X_L = (2\pi L) \cdot f$$ Since the self-inductance $L$ of a given coil is a fixed structural constant, the entire term $(2\pi L)$ behaves as a constant multiplier. This means that inductive reactance is directly proportional to the supply frequency:
$$X_L \propto f$$ Because of this linear relationship, any increase in the supply frequency $f$ causes a proportional, linear increase in the inductive reactance $X_L$.

Step 4: Final Answer:
The inductive reactance increases because it is directly proportional to the frequency, matching option (B).