Question

A light bulb and an open coil inductor are connected in series across an ac source of variable frequency. How will the glow of the bulb be affected when an iron bar is inserted inside the coil ? Justify your answer. Assume that other factors remain unchanged.

Hint:

Iron heavily amplifies localized magnetic flux linkage, acting as a massive multiplier for physical inductance; always strongly associate soft iron core insertion directly with significantly increased inductive reactance.
Think of the inductor exactly as a frequency-dependent resistor; increasing its "resistance" strictly throttles the overall current.

Answer 1

Concept:
• The visible brightness or visual glow of a standard resistive light bulb is strictly determined by the real power seamlessly dissipated across its internal filament, heavily dependent on the RMS current ($P = I_{rms}^2 R$).

• In a practical series AC circuit containing resistance and inductance, the driving operating current is meticulously governed by the total circuit impedance.

• The total impedance mathematically adjusts based on the inductive reactance, which is fiercely dependent on the physical inductance of the inserted coil.

Step 1: Understand the Initial State
The total electrical impedance $Z$ of the operating series circuit is robustly formulated as $Z = \sqrt{R_{bulb}^2 + X_L^2}$, where $X_L = \omega L$ physically represents the inductive reactance.
Initially, the inductor is an open air-core coil, meaning it has a relatively low baseline self-inductance $L_0$, dictated largely by the magnetic permeability of free space $\mu_0$.
The circuit draws a specific steady RMS current strictly based on this baseline impedance, causing the bulb to visibly glow with a certain stable brightness.

Step 2: Analyze the Effect of Inserting the Iron Bar
When a highly permeable soft iron bar is deliberately and deeply inserted inside the open coil, it forcibly completely replaces the air core with an iron core.
Soft iron intrinsically possesses a magnetic permeability ($\mu$) that is thousands of times significantly higher than that of empty air.
Because the physical self-inductance $L$ of a coil is mathematically strictly proportional to the permeability of its core material ($L \propto \mu$), introducing the iron bar drastically increases the fundamental self-inductance $L$ of the inductor coil.
As the self-inductance $L$ surges heavily upward, the inductive reactance $X_L$ proportionately and aggressively spikes up.

Step 3: Conclude the Effect on Bulb Brightness
Consequently, due to the massively inflated inductive reactance, the overall total impedance $Z$ of the entire series circuit substantially and noticeably increases.
Because the applied driving AC voltage source is held securely constant by definition of the problem, a much higher total impedance actively chokes the flow of electrons, strictly decreasing the operational RMS current $I_{rms}$ flowing continuously through the interconnected bulb.
With a noticeably reduced driving current, the actual thermal power actively dissipated by the glowing bulb ($P = I_{rms}^2 R_{bulb}$) heavily drops.
Since power strictly dictates brightness, the visual glow of the light bulb will dramatically and visibly decrease.