JEE Physics 2025 Question with Solution

Given: Assertion (A): A choke coil has large inductance and small resistance, and it is used with fluorescent mercury-tube fittings. Reason (R): the voltage across the tube is reduced by a factor

$$\frac{R}{\sqrt{R^2 + \omega^2 L^2}}$$

where $\omega$ is the supply frequency for resistor $R$ and inductor $L$.

Find: Which option correctly describes the truth value of Assertion (A) and Reason (R).

Explanation: The assertion is true. A choke coil indeed has large inductance and small resistance. In fluorescent tube circuits, it is used mainly to limit the alternating current without causing large power loss as an ordinary resistor would. If household supply is connected directly to the mercury tube, excessive current can flow and damage the tube.

The reason is false. The expression

$$\frac{R}{\sqrt{R^2 + \omega^2 L^2}}$$

does not correctly explain the working of the choke coil in protecting the tube. A choke coil primarily works through its inductive reactance

$$X_L = \omega L$$

which limits current in the AC circuit. Its main role is not simply to reduce the tube voltage by the stated factor. Therefore, the reason does not correctly represent the function of the choke coil.

Conclude: Assertion (A) is true but Reason (R) is false. The correct option is D.

Given:

• Assertion (A): A choke coil is simply a coil having a large inductance but a small resistance. Choke coils are used with fluorescent mercury-tube fittings. If household electric power is directly connected to a mercury tube, the tube will be damaged.
• Reason (R): By using the choke coil, the voltage across the tube is reduced by a factor

$$\frac{R}{\sqrt{R^2 + \omega^2 L^2}}$$

where $\omega$ is the frequency of the supply across resistor $R$ and inductor $L$.

Find: Whether Assertion (A) and Reason (R) are true or false.

1. Analyze Assertion (A): A choke coil is designed to have high inductance and low resistance. Its purpose in AC circuits such as fluorescent lamps is to limit current with small power dissipation. Therefore, the assertion is correct.

2. Interpret the circuit principle: In an AC circuit containing inductance $L$, the opposition to current is due to inductive reactance

$$X_L = \omega L$$

So the current is controlled by reactance rather than by large resistance.

3. Analyze Reason (R): The stated factor

$$\frac{R}{\sqrt{R^2 + \omega^2 L^2}}$$

is associated with voltage or current relations in a series $L-R$ circuit, but it is not the correct explanation for why a choke coil protects the fluorescent tube. The choke coil primarily limits current and also helps in the starting process of the tube. Hence the reason is false in the present context.

4. Final conclusion: Assertion (A) is true, but Reason (R) is false.

Therefore, the correct option is D.