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: Recall what inductive reactance is.
Inductive reactance $X_L$ is the opposition an inductor offers to alternating current; the faster the current alternates, the harder the inductor pushes back.
Step 2: Write its formula.
$$X_L = \omega L = 2\pi f L,$$ where $f$ is the supply frequency and $L$ is the inductance.
Step 3: Identify the constant part.
For a given coil, $L$ is fixed, so the combination $2\pi L$ is just a constant multiplier.
Step 4: Extract the proportionality.
This leaves $$X_L \propto f,$$ a simple direct (linear) proportionality.
Step 5: Predict the effect of raising $f$.
Because the relationship is linear, doubling the frequency doubles $X_L$; there is no square or inverse behaviour.
Step 6: State the conclusion.
So increasing the frequency increases the inductive reactance in direct proportion to the frequency.
\[ \boxed{X_L \propto f\ \text{(increases directly with } f)} \]