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: 

1. an iron bar is inserted inside the coil, and
2. the frequency of the source is decreased? 

Justify your answers. Assume that in each above case other factors remain unchanged.

Answer 1

The brightness of the bulb depends on the current flowing in the circuit.

The inductive reactance is given by:

XL = ωL

= 2πfL

(I) When an iron bar is inserted inside the coil:

• Inserting an iron core increases the inductance L.
• As a result, the inductive reactance X_L​ increases.
• This increases the total impedance of the circuit, causing the current to decrease.
• Because the bulb’s brightness depends on current, the bulb glows less brightly (its brightness decreases).

(II) When the frequency is decreased:

From the relation XL = 2πfL

• If the frequency f decreases, the inductive reactance X_L​ decreases.
• Lower reactance reduces the opposition to current, so the current increases.
• As a result, the bulb glows more brightly (its brightness increases).