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 (R / √(R²+ω² L²)), where ω is 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 the light of the above statements, choose the most appropriate answer from the options given below :

Solution

Physics sir · 4 steps

Treat the tube as a resistor R in series with the choke L: the choke takes its share of voltage, not power.

1. Model the circuit. The glowing tube behaves like a resistance R, and the choke is a pure inductance L in series with it. Both carry the same current I.

   I = V/√(R²+ω²L²) ⇒ V_R = IR = V R/√(R²+ω²L²)

2. Check the Reason. The factor R/√(R²+ω²L²) is less than 1, so the tube gets less than the supply voltage. With no choke, L = 0, the factor becomes 1 and the full supply voltage sits across the tube. So (R) is true.
3. Check the Assertion. A choke has large L and small resistance, so it cuts the voltage while wasting very little energy as heat. Connected straight to the mains, the tube takes the full voltage and gets damaged. So (A) is true.
4. So. (R) gives the exact reason the tube is safe with a choke and damaged without it. Both are true and (R) explains (A), which is option (b).

The idea to keep. In a series LR circuit the voltage divides like phasors: V_R = V R/√(R²+ω²L²). An inductor drops voltage with almost no heat loss, which is why chokes beat resistors.

Answer from the NTA final answer key. Solution by PrepWiser.