Question

A coil of self-inductance L is connected in series with a bulb B and an AC source. Brightness of the bulb decreases when:
a. Frequency of the AC source is decreased
b. Number of turns in the coil is reduced
c. Capacitance of reactance ${X_C} = {X_L}$ included in the same circuit
d. An iron rod is inserted in the coil

Answer 1

Hint: The property of a component that opposes the change in flow of current through it. If the current in a coil of a wire increases, then they will produce an emf which restricts the current. The inductance of a coil follows Faraday's law. Using the above definition determine when the bulb brightness reduces.

Complete step by step solution:
If the current in a coil of a wire increases, then they will produce an emf which restricts the current. Then by applying Kirchhoff's voltage law we see the effect of this emf on the circuit equation. Emf opposes the current change and is an example of Lenz's law. The inductance of a coil follows Faraday's law.

Inductor is produced by a self-induced emf due to their changing magnetic field. The property of the coil due to which it opposes the change of current in the other coil is called mutual inductance between two coils. When the current in the other coil or neighboring coil changes, a changing flux emf is induced in the coil. It is called mutual induced emf. The mutual inductance depends on cross sectional area, closeness of two coils and number of turns in the secondary coil.

The iron rod which is inserted inside the bulb, the magnetic field in the coil will magnetize the iron rod and thus increase the magnetic field in it. Then we know that inductance of the coil will increase. Therefore, the inductive reaction of the coil inside the bulb will increase also. Due to the result a fraction of the applied AC source feels like it is appearing across the inductor, thus leaving a less voltage across the bulb. By inserting an iron rod in the coil, inductance increases, impedance also increases but brightness decreases.

Hence, the correct answer is option (D).

Note: A galvanometer connected to the coil measures the induced emf. The flux linking with other coils changes when the current flowing through the primary coil is changed to the value of variable resistor $R$. Inductor is produced by a self-induced emf due to their changing magnetic field.