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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 $$\left(R/\sqrt{R^{2}+\omega^{2}L^{2}}\right)$$, where ω 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 :
For the fluorescent tube modeled as a resistor $$R$$ connected in series with a choke coil of inductance $$L$$:
$$Z = \sqrt{R^2 + \omega^2 L^2}$$
The current through the series circuit:
$$I = \frac{V}{Z} \implies I = \frac{V}{\sqrt{R^2 + \omega^2 L^2}}$$
Voltage across the tube (resistor $$R$$):
$$V_R = I \cdot R \implies V_R = V \cdot \left(\frac{R}{\sqrt{R^2 + \omega^2 L^2}}\right)$$
Without the choke coil ($$L=0$$):
$$V_R = V$$
Since a choke coil has high $$L$$ and low internal resistance, it safely reduces the voltage across the tube via reactance without dissipating significant thermal energy ($$P_{\text{avg}} = VI \cos\phi \approx 0$$).
Thus, Assertion (A) is true, Reason (R) is true, and (R) provides the correct physical mechanism for why the tube is protected.
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