ABUNDANT ELECTRICITY

Water flows from mountain top to valley down. All fluids flow from high pressure to low pressure. Heat flows from high temperature to low temperature. Similarly, the electrons flow from surplus point to starving point. In chemical reactions of a battery, there are more electrons at negative electrode and there is lack of electrons at positive electrode. Then the electrons try to flow from negative to positive electrode. When we connect negative and positive point by a wire, the current (electrons) flow from high electric potential to low electric potential. (Note: Electrons flow from negative to positive end and the conventional current is taken to flow from positive to negative).
Resistance: We know the current flows through the metal wire. The atoms in the metal are never at rest. They vibrate due to temperature. The electrons that move through these vibrating atoms get hits. So the metal atoms offer “resistance” to the current.

So the ohm’s law says,

"Electric current = potential difference between ends/ resistance".It means the electric current increases as the voltage (potential difference) increases. But it decreases as the resistance increases.

If we cool down the conductor (wire), the atomic vibrations slow down. At a particular temperature the atoms may comes to stand still. Then the electrons can fly through the wire without hindrance. Now the resistance of the conductor is almost zero. This conductor is called superconductor. Now, what are the consequences?

Current = Voltage/ resistance = V/0= infinity.

That means, once the current is setup in the superconductor it will go on for a very long time. There will be no loss of energy. In ordinary conductor, the electrons collide with atoms and loss energy in the form of heat and sound. Superconductor is now possible at very low temperature. But, still elusive at normal temperature. Once we have superconductor in room temperature, the electrical energy can be distributed without much loss, appliances can work with less waste. We can make super magnet which can levitate a train and move us fast and many more.

May the research in superconductivity be successful.

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LISSAJOUS FIGURES

Definition: "When a particle is subjected to two sine wave motion or two oscillatory motion at right angles, the particle describes lissajous figures". We know sine wave motion and circular motion is basically same. Hence we draw two circles A and B perpendicular to each other. The circle B rotates twice faster than circle A. That is, frequency of circle B is two times than that of A. A particle at the intersection of two circles is subjected to two sine wave motion A and B at 90 degree simultaneously. The particle will describe figures depending on the frequency and phase of A and B . In our case, the ratio of frequency is 1:2 and the two waves are in phase. To draw lissajous figures : A moving point in both the circles are chosen. Here we should remember; during the time taken by the circle A to complete one rotation, circle B completes two. Hence the points are marked on the circles according to their speed. Then straight lines

THE PARABOLA

A jet of water shooting from a hose pipe will follow a parabolic path. What is the so special about parabola. Y= x^2 Draw a graph for the above equation. It will result in a parabola. This parabola is also called unit parabola. Any equation involving square will yield a parabola. Example: Y = 2x^2 +3x+3 (also called quadratic equation) X= 2 and -2, both satisfies the equation 4 = X^2. Parabolic equations always have two solutions. Any motion taking place freely under gravity follows parabolic path. Examples: An object dropped from a moving train, A bomb dropped from flying plane, A ball kicked upwards. If a beam of light rays fall on the parabolic shaped mirror, they will be reflected and brought to focus on a point. This fact is made use of in Dish Antenna, Telescope mirrors, etc. Inverted parabola shape is used in the construction of buildings and bridges. Because the shape is able to bear more weight. A plane

CASINO'S GAME

Let us find out how the casino survives with mathematics. Say, your friend invite you for a game of dice. You must bet (wager) 2 dollars. If you roll 'six' you will get back 8 dollars. The game will go on for 30 rounds. All sounds good. The probability of rolling 'six' is 1/6. Since the game will be played for 30 times, the 'expected win' is 30*1/6 = 5. That is, you are expected to win 5 rounds out of 30. Hence your gain will be 5 * 8 =40 dollars. ok. This also implies that you will loose 25 rounds. Hence your loss will be 25*2 =50 dollars. Your net gain will be gain-less = 40-50 = -10 dollars. For 30 rounds, the loss is -10 dollars, Hence, for one round =-10/30 = -1/3 dollars. There will be a loss of -1/3 or 0.33 dollars per round. It is not a fair game. Let us make a simple formula to calculate 'Pay out per round\. The probability for a win = p The pay-out in case of win = V No. of rounds = n The expect

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