Assertion: The alternating current lags behined the e.m.f. by a phase angle of `pi//2`, when `AC` flows through an inductor.
Reason: The inductive reactance increases as the frequency of `AC` source decreases.

Options

A. a.If both assertion and reason are ture and reason is the correct explanation of assertion
B. b.If both assertion and reason are true but reason is not the correct explanation of assertion
C. c.If assertion is true but reason is false
D. d.If both assertion and reson are false.

Explanation

To solve the question, we need to analyze both the assertion and the reason provided.

### Step 1: Analyze the Assertion
The assertion states that "The alternating current lags behind the e.m.f. by a phase angle of π/2 when AC flows through an inductor."

- In an inductor, the voltage across the inductor (V_L) leads the current (I) by a phase angle of π/2. This means that the current lags behind the voltage by π/2.
- Mathematically, if we express the current as \( I = I_0 \sin(\omega t) \), then the voltage across the inductor can be expressed as:
\[ V_L = L \frac{dI}{dt} = L I_0 \omega \cos(\omega t) = L I_0 \omega \sin\left(\omega t + \frac{\pi}{2}\right) \]
- From this, we can see that the current lags the voltage by π/2. Therefore, the assertion is **True**.

### Step 2: Analyze the Reason
The reason states that "The inductive reactance increases as the frequency of the AC source decreases."

- Inductive reactance (X_L) is given by the formula:
\[ X_L = \omega L = 2\pi f L \]
where \( \omega \) is the angular frequency and \( f \) is the frequency of the AC source.
- From this formula, we can see that as the frequency (f) decreases, the inductive reactance (X_L) also decreases. Therefore, the reason is **False**.

### Conclusion
- The assertion is True, and the reason is False. Therefore, the correct answer is option C: Assertion is true but reason is false.