Assignment in Physics:

Who Discovered Electricity ? From the writings of Thales of Miletus it appears that Westerners knew as long ago as 600 B.C. that amber becomes charged by rubbing. But other than that, there was little real progress until the English scientist William Gilbert in 1600 described the electrification of many substances and coined the term "electricity" from the Greek word for amber.

As a result, Gilbert is called the father of modern electric power. In 1660, Otto von Guericke invented a crude machine for producing static electricity. It was a ball of sulfur, rotated by a crank with one hand and rubbed with the other. Successors, such as Francis Hauksbee, made improvements that provided experimenters with a ready source of static electricity. Today's highly developed descendant of these early machines is the Van de Graaf generator, which is sometimes used as a particle accelerator. Robert Boyle realized that attraction and repulsion were mutual and that electric force was transmitted through a vacuum. Stephen Gray distinguished between conductors and nonconductors. C. F. Du Fay recognized two kinds of power, which Benjamin Franklin and Ebenezer Kinnersley of Philadelphia later named positive and negative.

Progress quickened after the Leyden jar was invented in 1745 by Pieter van Musschenbroek. The Leyden jar stored static electricity, which could be discharged all at once. In 1747 William Watson discharged a Leyden jar through a circuit, and comprehension of the current and circuit started a new field of experimentation. Henry Cavendish, by measuring the conductivity of materials (he compared the simultaneous shocks he received by discharging Leyden jars through the materials), and Charles A. Coulomb, by expressing mathematically the attraction of electrified bodies, began the quantitative study of electric power.

Depite what you have learned, Benjamin Franklin did not "discover" electric power. In fact, electric power did not begin when Benjamin Franklin at when he flew his kite during a thunderstorm or when light bulbs were installed in houses all around the world.

The truth is that electric power has always been around because it naturally exists in the world. Lightning, for instance, is simply a flow of electrons between the ground and the clouds. When you touch something and get a shock, that is really static electricity moving toward you.

Power Personalities

 

Benjamin Franklin

Ben Franklin was an American writer, publisher, scientist and diplomat, who helped to draw up the famous Declaration of

Independence and the US Constitution. In 1752 Franklin proved that lightning and the spark from amber were one and the same thing. The story of this famous milestone is a familiar one, in which Franklin fastened an iron spike to a silken kite, which he flew during a thunderstorm, while holding the end of the kite string by an iron key. When lightening flashed, a tiny spark jumped from the key to his wrist. The experiment proved Franklin's theory.

 

Galvani and Volta

In 1786, Luigi Galvani, an Italian professor of medicine, found that when the leg of a dead frog was touched by a metal knife, the leg twitched violently. Galvani thought that the muscles of the frog must contain electric signals. By 1792 another Italian scientist, Alessandro Volta, disagreed: he realised that the main factors in Galvani's discovery were the two different metals - the steel knife and the tin plate - apon which the frog was lying. Volta showed that when moisture comes between two different metals, electric power is created. This led him to invent the first electric battery, the voltaic pile, which he made from thin sheets of copper and zinc separated by moist pasteboard.

In this way, a new kind of electric power was discovered, electric power that flowed steadily like a current of water instead of discharging itself in a single spark or shock. Volta showed that electric power could be made to travel from one place to another by wire, thereby making an important contribution to the science of electricity. The unit of electrical potential, the Volt, is named after Volta.

 

Michael Faraday

The credit for generating electric current on a practical scale goes to the famous English scientist, Michael Faraday. Faraday was greatly interested in the invention of the electromagnet, but his brilliant mind took earlier experiments still further. If electricity could produce magnetism, why couldn't magnetism produce electric power.

In 1831, Faraday found the solution. Electricity could be produced through magnetism by motion. He discovered that when a magnet was moved inside a coil of copper wire, a tiny electric current flows through the wire. Of course, by today's standards, Faraday's electric dynamo or electric generator was crude, and provided only a small electric current be he discovered the first method of generating electric power by means of motion in a magnetic field.

 

Thomas Edison and Joseph Swan

Nearly 40 years went by before a really practical DC (Direct Current) generator was built by Thomas Edison in America. Edison's many inventions included the phonograph and an improved printing telegraph. In 1878 Joseph Swan, a British scientist, invented the incandescent filament lamp and within twelve months Edison made a similar discovery in America.

Swan and Edison later set up a joint company to produce the first practical filament lamp. Prior to this, electric lighting had been my crude arc lamps.

Edison used his DC generator to provide electricity to light his laboratory and later to illuminate the first New York street to be lit by electric lamps, in September 1882. Edison's successes were not without controversy, however - although he was convinced of the merits of DC for generating electricity, other scientists in Europe and America recognised that DC brought major disadvantages.

 

George Westinghouse and Nikola Tesl

Westinghouse was a famous American inventor and industrialist who purchased and developed Nikola Tesla's patented motor for generating alternating current. The work of Westinghouse, Tesla and others gradually persuaded American society that the future lay with AC rather than DC (Adoption of AC generation enabled the transmission of large blocks of electrical, power using higher voltages via transformers, which would have been impossible otherwise). Today the unit of measurement for magnetic fields commemorates Tesla's name.

 

James Watt

When Edison's generator was coupled with Watt's steam engine, large scale electricity generation became a practical proposition. James Watt, the Scottish inventor of the steam condensing engine, was born in 1736. His improvements to steam engines were patented over a period of 15 years, starting in 1769 and his name was given to the electric unit of power, the Watt.

Watt's engines used the reciprocating piston, however, today's thermal power stations use steam turbines, following the

Rankine cycle, worked out by another famous Scottish engineer, William J.M Rankine, in 1859.

 

Andre Ampere and George Ohm

Andre Marie Ampere, a French mathematician who devoted himself to the study of electricity and magnetism, was the first to explain the electro-dynamic theory. A permanent memorial to Ampere is the use of his name for the unit of electric current.

George Simon Ohm, a German mathematician and physicist, was a college teacher in Cologne when in 1827 he published, "The galvanic Circuit Investigated Mathematically". His theories were coldly

received by German scientists but his research was recognised in Britain and he was awarded the Copley Medal in 1841. His name has been given to the unit of electrical resistance.

2.

The ability to repair basic house wiring in you home is a skill you can acquire. Knowing how circuits work and what can be done with them is useful knowledge. Wiring in a residential house is not that complicated, but it can be dangerous. Proper understanding and cautions are required.

 

Balls, Arrows, Missiles and Stones

If you throw a ball (or shoot an arrow, fire a missile or throw a stone) it will go up into the air, slowing down as it goes, then come down again ...

... and a Quadratic Equation tells you where it will be!

 Example: Throwing a Ball

A ball is thrown straight up, from 3 m above the ground, with a velocity of 14 m/s. When does it hit the ground?

Ignoring air resistance, we can work out its height by adding up these three things:

The height starts at 3 m:   3

It travels upwards at 14 meters per second (14 m/s):   14t

Gravity pulls it down, changing its speed by about 5 m/s per second (5 m/s2):   -

5t2

(Note for the enthusiastic: the -5t2 is simplified from -(½)at2 with a=9.81 m/s2)

   

Add them up and the height h at any time t is:

h = 3 + 14t - 5t2

And the ball will hit the ground when the height is zero:

3 + 14t - 5t2 = 0

Which is a Quadratic Equation ! In "Standard Form" it looks like:

-5t2 + 14t + 3 = 0

 

Example: New Sports Bike

You have designed a new style of sports bicycle!

Now you want to make lots of them and sell them for profit.

Your costs are going to be:

$700,000 for manufacturing set-up costs, advertising, etc

$110 to make each bike

Based on similar bikes, you can expect sales to follow this "Demand Curve":

Unit Sales = 70,000 - 200P

Where "P" is the price.

For example, if you set the price:

at $0, you would just give away 70,000 bikes at $350, you would not sell any bikes at all. at $300 you might sell 70,000 - 200×300 =

10,000bikes

 

So ... what is the best price? And how many should you make?

Let us make some equations!

How many you sell depends on price, so use "P" for Price as the variable

Unit Sales = 70,000 - 200P Sales in Dollars = Units × Price = (70,000 - 200P) × P = 70,000P - 200P2

Costs = 700,000 + 110 x (70,000 - 200P) = 700,000 + 7,700,000 - 22,000P = 8,400,000 - 22,000P

Profit = Sales-Costs = 70,000P - 200P2 - (8,400,000 - 22,000P) = -200P2 + 92,000P - 8,400,000

Profit = -200P2 + 92,000P - 8,400,000

Example: Small Steel Frame

Your company is going to make frames as part of a new product they are launching.

The frame will be cut out of a piece of steel, and to keep the weight down, the final area should be 28 cm2

The inside of the frame has to be 11 cm by 6 cm

What should the width x of the metal be?

Area of steel before cutting:

Area = (11 + 2x) × (6 + 2x) cm2

Area = 66 + 22x + 12x + 4x2

Area = 4x2 + 34x + 66

Area of steel after cutting out the 11 × 6 middle:

Area = 4x2 + 34x + 66 - 66Area = 4x2 + 34x

Let us solve this one graphically!

Here is the graph of 4x2 + 34x :

The required area of 28 is shown as a horizontal line.

 

The area equals 28 cm2 when:

 

x is approximately -9.3 or 0.8

The negative value of x make no sense, so the answer is:

x = 0.8 cm (approx.)

 

Example: River Cruise

A 3 hour river cruise goes 15 km upstream and then back again. The river has a current of 2 km an hour. What is the boat's speed and how long was the upstream journey?

There are two speeds to think about: the speed the boat makes in the water, and the speed relative to the land:

Let x = the boat's speed in the water (km/h) Let v = the speed relative to the land (km/h)

Because the river flows downstream at 2 km/h:

when going upstream, v = x-2 (its speed is reduced by 2 km/h)

when going downstream, v = x+2 (its speed is increased by 2 km/h)

We can turn those speeds into times using:

time = distance / speed

(if you travel 8 km at 4 km/h it would take 8/4 = 2 hours, right?)

And we know the total time is 3 hours:

total time = time upstream + time downstream = 3 hours

Put all that together:

total time = 15/(x-2) + 15/(x+2) = 3 hours

Now we use our algebra skills to solve for "x".

First, get rid of the fractions by multiplying through by (x-2)(x+2):

3(x-2)(x+2) = 15(x+2) + 15(x-2)

Expand everything:

3(x2-4) = 15x+30 + 15x-30

Bring everything to the left and simplify:

3x2 - 30x - 12 = 0

It is a Quadratic Equation! Let us solve it using the Quadratic Formula:

Where a, b and c are from the Quadratic Equation in "Standard Form": ax2 + bx + c = 0

Solve 3x2 - 30x - 12 = 0

Coefficients are:   a = 3, b = -30 and c = -12     

Quadratic Formula:   x = [ -b ± √(b2-4ac) ] / 2a

     

Put in a, b and c:   x = [ -(-30) ± √((-30)2-4×3×(-12)) ] / (2×3)

     Solve:  x = [ 30 ± √(900+144) ] / 6

    x = [ 30 ± √(1044) ] / 6    x = ( 30 ± 32.31 ) / 6    x = -0.39 or 10.39

 

Answer: x = -0.39 or 10.39 (to 2 decimal places)

Example: Resistors In Parallel

Two resistors are in parallel, like in this diagram:

The total resistance has been measured at 2 Ohms, and one of the resistors is known to be 3 ohms more than the other.

What are the values of the two resistors?

The formula to work out total resistance "RT" is:

1  =

1  +

1

RT R1 R2

In this case, we have RT = 2 and R2 = R1 + 3

1

  =

1

  +

1

2 R1R1+3

Now, let us set about solving this:

Get rid of the fractions by multiplying 

all terms by 2R1(R1 + 3): 

2R1(R1 + 3)

=

2R1(R1 + 3)

+

2R1(R1 + 3)

2 R1 R1+3    

Simplify:   R1(R1 + 3) = 2(R1 + 3) + 2R1

     Expand to:   R1

2 + 3R1 = 2R1 + 6 + 2R1

     Bring all terms to the left:   R1

2 + 3R1 - 2R1 - 6 - 2R1 = 0

     Simplify:   R1

2 - R1 - 6 = 0

Yes! A Quadratic Equation !

Let us solve it using our Quadratic Equation Solver.

Enter 1, -1 and -6 And you should get the answers -2 and 3

R1 cannot be negative, so R1 = 3 Ohms is the answer.

The two resistors are 3 ohms and 6 ohms.