Question

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). 

Assertion (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 \( L \). If the choke coil were not used, the voltage across the resistor would be the same as the applied voltage.

In light of the above statements, choose the most appropriate answer from the options given below:

• A. Both (A) and (R) are true and (R) is the correct explanation of (A)
• B. (A) is false but (R) is true
• C. Both (A) and (R) are true but (R) is not the correct explanation of (A)
• D. (A) is true but (R) is false

Hint:

Choke coils are used to limit current in devices like fluorescent tubes, but the explanation involving voltage reduction is not correct in this context.

Answer 1

The Correct Option is D

Assertion (A): A choke coil, characterized by high inductance and low resistance, is employed in fluorescent mercury-tube fittings. Direct connection of household electric power to a mercury tube would result in damage.

Reason (R): The voltage across the tube is diminished by a factor of \( \frac{R}{\sqrt{R^2 + \omega^2 L^2}} \) when a choke coil is utilized, where \( \omega \) represents the supply frequency across resistor \( R \) and inductor \( L \). Without the choke coil, the voltage across the resistor would equal the applied voltage.

Explanation:

Assertion (A) is accurate. A choke coil indeed possesses high inductance and minimal resistance. Its primary use in fluorescent tube lighting is to regulate current without significant power dissipation, a drawback of using resistors. Applying household power directly to a mercury tube would lead to excessive current and subsequent damage.

However, Reason (R) is incorrect. The formula \( \frac{R}{\sqrt{R^2 + \omega^2 L^2}} \) describes current division in AC circuits involving reactance and resistance. The choke coil's function is not primarily voltage reduction via this mechanism; rather, its inductive reactance, dependent on frequency \(\omega\) and inductance \(L\), limits current. The voltage drop across the inductive choke is not the sole protective element for the fluorescent tube; its inductive reactance is the key factor in preventing damage by controlling current flow.

Therefore, the correct response is:

(A) is true but (R) is false