IIT JEE Physics (1978-2018: 41 Years) Topic-wise Complete Solutions

# Put Me Off!

## Introduction

Current in an AC circuit depends on the circuit elements. These circuit elements may be the inductor, resistor or capacitor or a combination of two or more of them. This demonstration shows the dependence of this current on the inductance of the inductor.

## Apparatus

Inductor (Contactor coil), ordinary torch bulb, power source (AC source), cycle spokes and connecting wires

## Procedure

• Connect one end of the coil of the inductor to the bulb and another end of the coil to one terminal of the AC source.
• Similarly connect the other end of bulb to the other terminal of the AC source. Now the inductor and bulb are connected in series and same current will flow through both of them. Why?
• Switch on the power source and see the bulb glow.
• Now your task is to put the bulb off without switching the circuit off.
• Put one cycle spoke in the space of the plastic frame of the coil. Do you see a decrease in the glow of bulb?
• Put more cycle spokes till you do not see the bulb glowing anymore.

## Discussion

We have made a series $$LR$$ circuit connected to an AC source. The impedance (obstruction to the current) offered by the circuit is given by $$Z=[(\omega L)^2 + (R)^2]^{1/2}$$, where $$L$$ is the self inductance of the inductor, $$R$$ is the resistance of mainly the bulb (neglecting the resistance of the windings of the inductor coil) and $$\omega$$ is the angular frequency of the AC source. Increase in this impedance will decrease the current in the circuit and hence decrease the glow of the bulb.

When we put cycle spokes inside the inductor core, the self inductance $$L$$ of the coil, which is dependent on the geometry of the coil and the material inside it, increases. Relative permeability of material in the core decides the self inductance. Earlier it was an air core inductor but putting cycle spokes in the space makes it air plus iron core inductor. Relative permeability of iron is much higher so the inductance increases substantially. Increase in this inductance leads to a greater impedance and a smaller current till the bulb stops glowing.

An alternative experiment: If a capacitor (say $$1000\,\mathrm{\micro{F}}$$) is also included in the series circuit making it an $$LCR$$ circuit, there is an increase in the glow of the bulb when cycle spokes are put in the core of the inductor coil. Why?