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

# Playing with Capacitors made from Kitchen Utensils

## Introduction

A capacitor is a combination of two conductors separated by a thin insulating material (called the dielectric). It can be charged by connecting the two conductors to a battery. The charge required to create a potential difference of 1 Volt between its conducting plates is called the capacitance of the capacitor. In this demonstration we will make capacitors with kitchen utensils and measure their capacitance in many combinations.

## Apparatus

Two similar flat bottomed steel thalis, wooden carrom board coins, three similar steel glasses, polythene sheet, newspaper, LCR meter.

## Procedure

### Thali capacitor:

1. Invert a steel thali and keep it on a table such that a small portion of it is over the edge of the table.
2. Attach a crocodile clip from below to the protruding portion of the thali and connect a copper wire to the clip.
3. Now put three carrom board coins on the thali and place another thali over it (face up).
4. Attach another crocodile clip to the upper thali and connect a copper wire to the clip.
5. Connect the two copper wires to an $$LCR$$ meter.
6. Measure its capacitance.
7. Put a newspaper in the gap between the two thalis and again measure its capacitance.

The capacitance shows a value in picofarads which increases when a newspaper is inserted in the air gap.

### Glass capacitor

1. Wrap a steel glass (glass 2) with a polythene sheet and put it inside another steel glass (glass 1).
2. Attach crocodile clips with copper wires connected to them to the rims of the two glasses.
3. Connect the two copper wires to the LCR meter and measure the capacitance (call it $$C_1$$).
4. Wrap another glass (glass 3) in a polythene sheet and put it inside glass 2.
5. Attach crocodile clip with copper wire connected to it to the rim of glass 3.
6. Now connect the wires of glass 1 and glass 3 to the LCR meter. Leave the wire of glass 2 free.
7. Measure the capacitance (call it $$C_2$$)
8. Connect the wires of glass 1 and glass 3 and measure the capacitance between this common terminal and glass 2 (call it $$C_3$$).

See that the capacitance $$C_2$$ is almost half the capacitance $$C_1$$ and the capacitance $$C_3$$ is almost double the capacitance $$C_1$$. All the capacitances measured are in picofarads.

## Discussion

In the arrangement made with the thalis, the steel thalis are the two conductors and placing carrom board coins creates an air gap which acts as the dielectric. Hence the arrangement acts as a capacitor. Putting paper in the air gap increases the capacitance as the dielectric constant of paper is higher than that of air. Capacitance $$C$$ of the capacitor is given by the expression $$C=K\epsilon_0 A/d$$ where $$\epsilon_0$$ is the permittivity of free space, $$A$$ is the area of the conductors, $$d$$ is the distance between the two plates and $$K$$ is the dielectric constant of the dielectric between the conductors. For air $$K = 1$$ and for paper $$K>1$$.

In the arrangement made with steel glasses, the steel glasses are the two conductors and the polythene acts as a dielectric. Hence it becomes a capacitor. The capacitance $$C_2$$ is almost half of $$C_1$$ as the arrangement makes it a series combination of two almost identical capacitors. The capacitance $$C_3$$ is double of $$C_1$$ as the arrangement this time makes it a parallel combination of two capacitors.

The equivalent capacitance $$C_{eq}$$ of $$N$$ identical capacitors each of capacitance $$C$$ is given by, $$C_{eq}= C/N$$ in series combination and $$C_{eq} = NC$$ in parallel combination.