Question 291: AC fundamentals

Question

A coil of self-inductance $L$ is connected in series with a bulb and an a. c. source. Brightness of the bulb decreases when

Accepted Answer

Let us analyze each option step by step as per NCERT methods:
The coil (inductor) has inductive reactance $X_L = 2\pi f L$.
The total impedance of the circuit is $Z = \sqrt{R^2 + X_L^2}$, where $R$ is the resistance of the bulb.
The brightness of the bulb depends on the current in the circuit:
$$ I = \frac{V}{Z} $$
More impedance $Z$ $\implies$ less current $\implies$ less brightness.
Option A:
An iron rod is inserted in the coil.
Inserting iron increases the core's permeability, which
increases inductance $L$
.
$X_L = 2\pi f L$ also increases.
Higher $X_L$ $\implies$ higher $Z$ $\implies$
current decreases
.
Brightness decreases.
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Option B:
Frequency of a.c. source is decreased.
$X_L = 2\pi f L$, so if frequency $f$
decreases
, $X_L$
decreases
.
Lower $X_L$ $\implies$ lower $Z$ $\implies$
current increases
.
Brightness increases.
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Option C:
Number of turns in the coil is reduced.
Inductance $L$ depends on the number of turns. If turns decrease, $L$ decreases.
$X_L$ decreases $\implies$ $Z$ decreases $\implies$
current increases
.
Brightness increases.
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Option D:
A capacitance of reactance $(X_C - X_L)$ is included in the same circuit.
If a
capacitor
is added
in series
, the total impedance becomes
$Z = \sqrt{R^2 + (X_L - X_C)^2}$.
If $X_C = X_L \implies Z = R$ (current maximum, brightness maximum).
If $X_C < X_L$, $Z$ is less compared to only $X_L$.
Including a capacitor generally decreases overall impedance
(except at resonance).
Brightness increases.
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Final answer:
The
brightness of the bulb decreases when an iron rod is inserted in the coil
.
Correct option: Option A

Answer

an iron rod is inserted in the coil.

Answer

frequency of a.c. source is decreased.

Answer

number of turns in the coil is reduced.

Answer

a capacitance of reactance $\left(\mathrm{X}_{\mathrm{C}}-\mathrm{X}_{\mathrm{L}}\right)$ is included in the same circuit.

AC fundamentals

A coil of self-inductance L is connected in series with a bulb and an a. c. source. Brightness of the bulb decreases when

Choose the correct answer: