JEE Main 2025 — Current Electricity Question with Solution

Assertion (A):

A choke coil is simply a coil having large inductance but 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.

A choke (or ballast) does have high inductance and low resistance.

In a fluorescent lamp (or mercury‐vapor lamp) circuit, the choke limits the current through the tube.

If we connect the tube directly to the full line voltage without any current-limiting device, excessive current will flow and damage the tube.

Therefore, (A) is true.

Reason (R):

By using the choke coil, the voltage across the tube is reduced by a factor

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

where $\omega$ is the supply frequency, and $R$ and $L$ are the resistance and inductance in series.

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

In a simple series R–L circuit (where $R$ represents the lamp’s effective resistance once conducting, and $L$ is the choke’s inductance), the total impedance is

$Z=\sqrt{R^2+(\omega L{)}^2}.$

The current is the same through $R$ and $L$. The fraction of the total supply voltage appearing across $R$ alone is

$\frac{V_R}{V_{\text{total}}}=\frac{IR}{IZ}=\frac{R}{\sqrt{R^2+(\omega L{)}^2}}.$

This shows that using a large inductance $L$ (the choke) can substantially reduce (or limit) the voltage—and hence the current—through the lamp.

Without the choke coil, the tube (treated here as a resistor once it starts conducting) would indeed see nearly the full line voltage, causing a large current that could destroy it.

Therefore, (R) is also true.

Does (R) correctly explain (A)?

(A) states why a choke coil is needed (to prevent the lamp from being damaged by excessive current).

(R) shows how the choke coil limits the voltage/current through the lamp—by giving the fraction of the supply voltage that appears across the lamp in a series R–L circuit.

Thus, (R) does provide the correct (physics-based) explanation: the choke’s inductive reactance drops a significant portion of the supply voltage, thereby protecting the lamp.

Hence, the correct option is:

$\boxed{\text{Option B: Both (A) and (R) are true and (R) is the correct explanation of (A).}}$