Capacitor pdf



A capacitor (originally known as a condenser) is a passive two-terminal electrical component used to store energy electro statically in an electric field. The forms of practical capacitors vary widely, but all contain at least two electrical conductors (plates) separated by a dielectric (i.e. insulator). The conductors can be thin films, foils or sintered beads of metal or conductive electrolyte, etc. The “non-conducting” dielectric acts to increase the capacitor’s charge capacity. A dielectric can be glass, ceramic, plastic film, air, vacuum, paper, mica, oxide layer etc. Capacitors are widely used as parts of electrical circuits in many common electrical devices. Unlike a resistor, an ideal capacitor does not dissipate energy. Instead, a capacitor stores energy in the form of an electrostatic field between its plates.

When there is a potential difference across the conductors (e.g., when a capacitor is attached across a battery), an electric field develops across the dielectric, causing positive charge +Q to collect on one plate and negative charge −Q to collect on the other plate. If a battery has been attached to a capacitor for a sufficient amount of time, no current can flow through the capacitor. However, if a time-varying voltage is applied across the leads of the capacitor, a displacement current can flow.









Capacitors are widely used in electronic circuits for blocking direct current while allowing alternating current to pass. In analogue filter networks, they smooth the output of power supplies. In resonant circuits they tune radios to particular frequencies. In electric power transmission systems, they stabilize voltage and power flow.

An ideal capacitor is wholly characterized by a constant capacitance C, defined as the ratio of charge ±Q on each conductor to the voltage V between them




My Experience at the Workshop


The word Workshop is very common in Auroville. Lots of workshops happen over the course of a year. But I never got the idea of attending any of the workshop(I also dont know why I didnt attend any and probably it never struck me).

Sanjeev then one day told us about a workshop called Stewardship for New Emergence (Monika Sharma’s workshop). He told us that the 1st stage of the workshop is for 9 days(I was like wow! 9 days!) and gave us a form to fill for the workshop. Just looking at the form made me feel that the workshop is going to be intense. Just filling up the form made me think a lot about myself.

The workshop was held over a period of 3 months(3 days a month).

We learnt about 40 tools in these 9 days. All the tools given in the workshop are very much related to everyone’s daily life. Every exercise given in the workshop would have somehow or the other happened in your life but I never have thought about how and why it happened, what I learnt is to differentiate the tools that was given.

For example, there was an exercise about ‘anger’. There are two types of anger(Destructive and Principled). This was the first time I heard about anger being differentiated into two types. All I knew about anger before was shouting and pouring emotions on someone(destructive anger). But after doing this exercise I came to know that sometimes even my anger was not destructive and I was Principled in my anger.

There was tool about ‘complaints’. We all listen to complaints made by others and get bored and agitated. But here i learnt to listen to the committments behind the complaints. It made me look at complaints made by other people on me in a dfiferent angle.

Like this i learnt a lot of new things that are needed for the growth of myself and the people around me. Just attending this 9 days(which was fully worth it) of workshop does not give someone a new life. It is important that I practice all the tools that I have learned.

Overall this workshop was totally a new and a different experience for me personally. I came to know more about myself and I think over these 9 days I have accomplished a New Emergence !!

Simple Motor With the 4th Graders


DSC_0455 DSC_0457DSC_0459To design a simple motor all we need is a number of batteries, neodymium magnets, metal screws or nails, and some copper wires (they do not get attracted by magnets, and they conduct electricity).


The 4th graders were super excited when Bala and I entered the class with a box on our hand. Then i explained that we would be doing a small experiment with magnets and some batteries. We split the class into four smaller groups and handed each group the required number of components. The explanation on how to connect the components was shown, and the children made their own motors. While doing the motor they realized that when the batteries polarity were reversed the direction of the spinning screw also reversed.




water-bowlsOnce the children were done with the motor, they did a puzzle on water and weighing.

” If you had a 5-liter bowl and a 3-liter bowl, and an unlimited access to water, how would you measure exactly 4 litres. ”

all came up with interesting ideas and explanations.

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Nullator and Norator


In electronics, a nullator is a theoretical linear, time-invariant one port defined as having zero current and voltage across its terminals. Nullators are strange in the sense that they simultaneously have properties of both a short (zero voltage) and an open current(zero current). They are neither current nor voltage sources, yet both at the same time.

Inserting a nullator in a circuit schematic imposes a mathematical constraint on how that circuit must behave, forcing the circuit itself to adopt whatever arrangements needed to meet the condition. For example, the inputs of an ideal operational amplifier(with negative feedback) behave like a nullator, as they draw no current and have no voltage across them, and these conditions are used to analyze the circuitry surrounding the operational amplifier.

A nullator is normally paired with a norator to form a nullor.

Two trivial cases are worth noting: A nullator in parallel with a norator is equivalent to a short (zero voltage any current) and a nullator in series with a norator is an open circuit (zero current, any voltage).



In electronics, a norator is a theoretical linear time invariant one port which can have an arbitrary current and voltage between its terminals. A norator represents a controlled voltage or current source with infinite gain.

Inserting a norator in a circuit schematic provides whatever current and voltage the outside circuit demands. For example, the output of an ideal opamp behaves as a norator, producing nonzero output voltage and current that meet circuit requirements despite a zero input.

A norator is often paired with a nullator to form a nullor.

Two trivial cases are worth noting: A nullator in parallel with a norator is equivalent to a short (zero voltage any current) and a nullator in series with a norator is an open circuit (zero current, any voltage).


Reference : Verhoeven C J M van Staveren A Monna G L E Kouwenhoven M H L & Yildiz E (2003)


Learning Algebra With the the help of scratch

After finished Geometry i was switched to Algebra. Mastering algebra is important for moving on to nearly all other types of mathematics in  school. However, even the most basic algebra skills can be tricky for beginners to understand the first time they encounter them. I was in the need to know their prior knowledge in algebra in order to build on that (if that was conceptual) or correct them (if that was misconception). So, I gave some equations to solve, asked some stories (Multiplication & Division) and gave them small puzzles  to understand their understandings in algebra.

Except few, all posses some sort of difficulties. Some of them could not able to interpret the question, some of them having difficulties in calculation part, Some were guessed the answers. From that i inferred they need more explanation to understand the concepts. So, i took them to computer lab to practise algebra using scratch programming. First, i gave an expression of 5x+10 and asked them to draw bar graphs in scratch,                                     where x = 1,2,3,4,…….10(with guidance).

Screenshot from 2015-03-13 08:23:18Screenshot from 2015-03-13 08:23:02

Then, i asked them to find out the value of x in the following equation 5x+10=70.

Screenshot from 2015-03-18 16:27:14 Screenshot from 2015-03-18 16:27:45

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What I was  inferred, they could learn(understand) the things comparatively quicker by programming than doing it manually (as procedural). Hence i decided to add one more concept on that just like fun by asking them to draw multi-stair case like structure by modifying the program   ( underScreenshot from 2015-03-13 12:22:31 guidance).


Screenshot from 2015-03-13 12:23:36

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Mathematics Experiments with 7th Grade Students

The lack of a good education ( sometimes, misunderstanding  or partial understanding of concepts)  is one of the biggest issue across the globe.  Having an educational infrastructure (i.e. schools) is only half the battle. Teacher training is crucial and often the missing element. In order to get a good education children need to have teaching methods which motivate and offer them freedom to learn while in school, and this is where the “chalk and talk” teaching fails.

“Chalk & Talk” is a formal method of teaching with a blackboard and the teacher’s voice as its focal point. This method is used in classrooms across the world. However, this formal and somewhat unimaginative teaching method has come under scrutiny, with many people suggesting that teachers should not rely solely on this technique if they want to engage and inspire their students. Another criticism is that this method of teaching tends to go with the pace of the fastest learner and can leave a lot of children behind. That is, this “Chalk & Talk” method fails to stimulate all the students’ interests in learning. Education needs to be more practical, should allow children to express themselves and learn independently at their own.

So we decided to handle the mathematics class with some programming tool like GeoGebra  ( used to do Geometry) and Sratch ( Syntax free programming). At my first class with 7th graders, i started with GeoGebra. Because, most of the students follow only the procedure not the concepts behind the procedure.

During that period, they learnt about how to draw Equilateral Triangle & Isosceles triangle in GeoGebra (under some different kinds of condition) and their properties. (Here, i enclosed some pictures of my students’ work in Geometry).Screenshot from 2015-03-12 15:35:07

Screenshot from 2015-03-12 15:38:38      This practice made the students to do their text book exercises by their own. Of course, I guess, it took me comparatively more time than “Chalk & Talk” method.

But It doesn’t matter when the students reproduced the things by their understanding.


My First Interaction with Children

My First Proper Interaction with Children (6th graders)

We made a device called ‘SpeeDE’ that measures the speed of an object. We thought that taking this device to school and showing it to the children would be something new to them. One day I took the device to the sixth graders. Everyone saw SpeeDe in my hand and were very eager to know about it.
I started with telling them simple stories on speed and distance.
Eg, I travelled at a speed of 20km/hr, how much distance would i have covered for 3 hrs?

Then i asked the students to make up their own stories. Lots of new stories were made up.
But they had difficulties in the units(km/hr, m/s). They were not completely comfortable with the units.
After most of them had finished telling thier own speed and distance story, it was time to measure something from our device. I started with dropping a pencil case from about a metre to measure the speed of that and asked them to guess the speed. All types of random answers came up.
Then i dropped it from about half a metre and then dropped it from close to the device. The students who were pretty close to right answer were really happy and excited.
Then i asked why does the speed vary when I drop the pencil case from different heights. Some managed to tell that as the height increases the speed of the object also increased which was pleasing to hear.
Then at the end of the class we measured the speed of their punch and kick etc..
Everything was totally a new experience for me. I came to know that handling a class is not that easy as i expected.
Students tend to get more engaged in the class when we bring hands on stuff or else its not that easy to handle a class !!

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The wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave’s shape repeats. It is usually determined by considering the distance between consecutive corresponding points of the same phase.


The above figure shows the wavelength at a certain time period(the figure is freezed)

In linear media, any wave pattern can be described in terms of the independent propagation of sinusoidal components. The wavelength λ of a sinusoidal waveform traveling at constant speed v is given by

λ = v/f

where v is called the phase speed (magnitude of the phase velocity) of the wave and f is the wave’s frequency. In a dispersive medium, the phase speed itself depends upon the frequency of the wave, making the relationship between wavelength and frequency nonlinear.

In the case of electromagnetic radiation such as light in free space, the phase speed is the speed of light, about . Thus the wavelength of a 100 MHz electromagnetic (radio) wave is about: divided by 108 Hz = 3 meter.

For sound waves in air, the speed of sound is 343 m/s (at room temperature and atmospheric pressure). The wavelengths of sound frequencies audible to the human ear (20 Hz–20 kHz) are thus between approximately 17 m and 17 mm, respectively. Note that the wavelengths in audible sound are much longer than those in visible light.

Difference between Wavelength and Time Period :

There are two variables. One is time and other distance.

We can draw a curve with respect to time and say the vertical displacement at a particular point which shows the period and amplitude. It is time variant at particular point.

We can also draw a curve with respect to distance at a particular time which shows the wavelength and amplitude.

More animations about wavelength are given :

Circle Using Scratch

Polar Form of a Circle :
The polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a fixed point and an angle from a fixed direction. Keeping the radius as constant value(as the radius of the circle of the cant change), the angle keeps on varying until the circle is complete.
Here, we have a circle with radius r.
Along the x- axis it is r cos angle and along the y-axis it is r sin angle.
x : r cos angle
y : r sin angle
Circle moved along the axis with radius r :
Three circles are shown in the figure.
Each circle has a radius of r(defined by the user).
Center Circle :
The circle at the center has origin of (0,0) and by using the polar form method a simple circle can be drawn by defining the radius r and the angle.
x = r cos angle
y = r sin angle
Circle on the top :
The circle on the top is along y axis. The origin of this circle is at the edge of the center circle on the y axis. So,the equation of this circle is
x = r cos angle
y = r+r sin angle
Circle on the right :
The circle on the right is along x axis. The origin of this circle is at the edge of the center circle on the x axis. So,the equation of this circle is
x = r+r cos angle
y = r sin angle
Drawing a Circle in Scratch using the Trigonometric Formula :
There are number ways to draw a circle in Scratch. Lets have a look at how to draw a circle using the Trigonometric formula(Polar form).
Simple way to make a circle is to use the Motion Scripts and to use the Move keys and angle (360 degree) etc..
Create Variables :
Example ,
Radius, r = 50
Sides( the more no of sides you put, the more it will look like a circle) = 80
Angle_step(to make it move in small angles) = 360/ sides
Angle = 0 degree
Use the Motion script to tell Scartch where you want to start the circle.
Here it is :
In the Loop :
Change the angle by the angle step( so that the angle changes everytime)
Use the formula :
x : r cos angle
y : r sin angle