Question

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

• A. an iron rod is inserted in the coil.
• B. frequency of the AC source is decreased
• C. number of turns in the coil is reduced.
• D. A capacitance of reactance XC = XL is included in the same circuit.

Answer 1

The Correct Option is A

To solve this problem, we need to examine what happens when different changes are made to the coil, bulb, and AC source circuit. Let's consider each option one by one.

1. Option: An iron rod is inserted in the coil.
   • Inserting an iron rod into the coil increases its inductance L because the magnetic permeability of iron is higher than that of air.
   • With higher inductance, the inductive reactance X_L = 2\pi f L also increases, where f is the frequency of the AC source.
   • A higher inductive reactance means less current flows through the circuit when connected to an AC source, because the impedance (total resistance) of the circuit increases.
   • Less current through the bulb means it receives less power, thereby reducing its brightness. Therefore, this option is correct.
2. Option: Frequency of the AC source is decreased.
   • Decreasing the frequency f decreases the inductive reactance X_L of the coil.
   • With less reactance, more current can flow through the circuit, potentially increasing the bulb's brightness, not decreasing it.
   • This option would generally increase brightness, so it is not correct.
3. Option: Number of turns in the coil is reduced.
   • Reducing the number of turns in the coil decreases its inductance L.
   • Less inductance leads to lower inductive reactance X_L, which allows more current to pass through the circuit.
   • This results in increased bulb brightness, so this option is not correct.
4. Option: A capacitance of reactance X_C = X_L is included in the same circuit.
   • Including a capacitance such that X_C = X_L causes resonant conditions in the circuit.
   • In resonance, the inductive and capacitive reactances cancel each other, maximizing the current in the circuit.
   • Maximized current increases the brightness of the bulb rather than decreasing it. Therefore, this option is not correct.

In conclusion, the brightness of the bulb decreases when an iron rod is inserted in the coil because it increases the coil's inductance and reduces the current through the circuit.