Question 206: Current Electricity

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 $\left(R / \sqrt{R^2+\omega^2 L^2}\right)$, where $\omega$ 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 :

Accepted Answer

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 mercuryÃ¢ÂÂ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
$\displaystyle \frac{R}{\sqrt{R^2 + (\omega L)^2}}$,
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 RÃ¢ÂÂL
circuit (where $R$ represents the lampÃ¢ÂÂs effective resistance once conducting, and $L$ is the chokeÃ¢ÂÂ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_{	ext{total}}} \;=\; \frac{I\,R}{I\,Z} \;=\; \frac{R}{\sqrt{R^2 + (\omega L)^2}}.      $
This shows that using a large inductance $L$ (the choke) can substantially reduce (or limit) the voltageÃ¢ÂÂand hence the currentÃ¢ÂÂ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 lampÃ¢ÂÂby giving the fraction of the supply voltage that appears across the lamp in a series RÃ¢ÂÂL circuit.
Thus, (R)
does
provide the correct (physics-based) explanation: the chokeÃ¢ÂÂs inductive reactance drops a significant portion of the supply voltage, thereby protecting the lamp.
Hence, the correct option is:
$ \boxed{	ext{Option B: Both (A) and (R) are true and (R) is the correct explanation of (A).}} $

Answer

(A) is true but (R) is false

Answer

Both $(\mathbf{A})$ and $(\mathbf{R})$ are true and $(\mathbf{R})$ is the correct explanation of $(\mathbf{A})$ 3.

Answer

Both $(\mathbf{A})$ and $(\mathbf{R})$ are true but $(\mathbf{R})$ is not the correct explanation of $(\mathbf{A})$

Answer

(A) is false but (R) is true

Current Electricity

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