A : For a practicval choke coil the power factor is very small.
R : In a practical choke coil the power dissipation reduces if frequency of the a.c. is increased.

Options

A. If both Assertion & Reason are true and the reason is the correct explanation of the assertion, then mark (1)
B. If both Assertion & Reason are true but the reason is not the correct explanation of the assertion, then mark (2)
C. If Assertion is true statement but Reason is false, then mark (3)
D. If both Assertion and Reason are false statement, then mark (4)

Answer

To analyze the given assertion and reason regarding a practical choke coil, let's break down the solution step by step.

### Step 1: Understand the Assertion
The assertion states that "For a practical choke coil, the power factor is very small."
- A choke coil is an inductive component used to limit the current in an AC circuit. In practical applications, especially in devices like tube lights, the choke coil is designed to reduce the voltage across the load.

**Hint:** Recall that the power factor (PF) is a measure of how effectively electrical power is being converted into useful work output.

### Step 2: Understand the Reason
The reason states that "In a practical choke coil, the power dissipation reduces if the frequency of the AC is increased."
- Power dissipation in an inductive circuit is related to the resistance (R) and the current flowing through it. As frequency increases, the inductive reactance (X_L = ωL) increases, leading to a higher impedance (Z = √(R² + X_L²)).

**Hint:** Consider how inductive reactance (X_L) affects the overall impedance of the circuit and how this relates to the power factor.

### Step 3: Analyze the Relationship Between Power Factor and Frequency
- The power factor (cos φ) is defined as the ratio of the resistance (R) to the impedance (Z):
\[ \text{PF} = \cos \phi = \frac{R}{Z} \]
- As frequency increases, X_L increases, which increases Z. If R remains constant, a larger Z results in a smaller power factor.

**Hint:** Think about how increasing the inductive reactance impacts the overall circuit behavior and the power factor.

### Step 4: Connect the Assertion and Reason
- Since the power factor is small in a practical choke coil due to the high inductive reactance at increased frequencies, the assertion is true.
- The reason correctly explains why the power factor is small: as frequency increases, the power dissipation decreases because the reactance increases, leading to a higher impedance and a lower power factor.

**Hint:** Reflect on how the relationship between frequency and inductive reactance plays a crucial role in determining the power factor.

### Step 5: Conclusion
Based on the analysis:
- Both the assertion and reason are true.
- The reason provides a correct explanation for the assertion.

Thus, the final conclusion is:
- **Assertion (A) is true.**
- **Reason (R) is true and correctly explains the assertion.**

### Final Answer:
Both the assertion and reason are true, and the reason is a correct explanation of the assertion.

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