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 statements regarding a practical choke coil, let's break down the assertions and reasoning step by step.

### Step 1: Understanding the Assertion
**Assertion (A):** For a practical choke coil, the power factor is very small.

- A choke coil is an inductor used in AC circuits to limit the current.
- The power factor (cos φ) in an AC circuit is defined as the ratio of the real power flowing to the load to the apparent power in the circuit.
- In a choke coil, which has significant inductance, the inductive reactance (X_L) is usually much larger than the resistance (R).
- This results in a small power factor, as the power factor is given by cos φ = R/Z, where Z is the impedance (Z = √(R² + X_L²)).

### Step 2: Understanding the Reason
**Reason (R):** In a practical choke coil, the power dissipation reduces if the frequency of the AC is increased.

- The inductive reactance (X_L) is given by the formula X_L = ωL, where ω is the angular frequency (ω = 2πf, with f being the frequency).
- If the frequency (f) increases, the inductive reactance (X_L) also increases.
- As X_L increases, the total impedance (Z) of the circuit increases, which leads to a decrease in the current (I) flowing through the circuit, given that V = IZ.
- Since the power dissipation (P) in an AC circuit is given by P = I_rms²R cos φ, if the current decreases, the power dissipation also decreases.

### Step 3: Conclusion
- Both the assertion and reason are true.
- The reason provided correctly explains the assertion regarding the choke coil's power factor and power dissipation.

### Final Answer
Both the assertion (A) and reason (R) are true, and the reason is the correct explanation of the assertion.

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