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Electrical Power Generation

While batteries are useful for portable electrical power, their one-time use is expensive and the amount of power produced is small compared to other forms of electrical generation. While solar cells are available for direct conversion of light into electricity, they too suffer from high relative cost and small power output. By far, the largest production of electrical production is electro-mechanical, i.e. the conversion of mechanical energy into electrical energy. No matter the ultimate source of energy, coal, oil, natural gas, nuclear, or hydroelectric, this energy is converted into mechanical work which turns a generator which produces electricity. It is this conversion between mechanical energy and electical energy which is the subject of this project.

Work and Power

One of the main uses of electricity is to produce motion. When we move something through a distance against a resisting force we do work. To move a weight against the force of gravity requires work:
W = m h g
where W is work, m is mass, h is the height through which the weight is lifted, and g is the gravitational constant (9.8 m/sec2). Let's consider the work needed to lift a 2 L soft drink bottle (approx. 2 kg) to a height of 1 meter against the force of gravity:
(2 kg)(1 m)(9.8 m/sec2)
= 19.6 kg m2/sec2
= 19.6 J

The unit of work is called the Joule. 1 J = 1 kg m2/sec2. The Joule is also the unit of energy. Energy is a general term, of which work and heat are two examples. How much work is needed for a 200 pound student to climb the staircase (76 steps) of Gilmer Hall? Each step is 6.25 inches, so
m h g = (200 pounds)(76 steps)(9.8 m/sec2)(454 g/pound)(1 kg/1000 g)(6.25 in/step)(2.54 cm/in)(1 m/100cm)
=10736 J
=10.7 kJ

This work is required whether we climb the steps quickly or slowly. But it is harder to climb the stairs quickly. We say that it requires more power to climb quickly than it does to climb slowly. Power is defined as the work done divided by the time it takes to do that work.
P = W/t

If we take 1 second to climb each step, we are using power at the rate of
10736 J/76 sec
=141 J/sec
= 141 Watt
The unit of power is the Watt, which is defined as 1 J/sec. If we climb more quickly, say, 4 steps per second, we will use power at the rate of
(10736 J/76 steps)(4 steps/sec)
=565 Watt

Well, what does this have to do with electricity? On the battery page, we discussed separating a redox reaction into two parts and requiring the electrons to do work as they pass through the wire on the way from the anode to the cathode. The power produced by a battery depends both on the voltage and on the charge. Here we make the connection between electrical work and mechanical work:
W = V C
C is the charge in Coulombs. 1 J = 1 Volt * 1 Coulomb. And how much charge is a Coulomb? Well, 1 mole of electrons has a charge of 96500 Coulombs. So, recalling our zinc acid cell, which had a voltage of .76 V and 2 moles of electrons for every mole of zinc, we could produce:
(0.76 V)(96500 C/mol e)(2 mole e/mol Zn)
=146680 VC = 146680 J = 147 kJ

For every mole of zinc consumed in our battery we can produce 147 kJ of work. If we produce this work in 1 sec, we will produce power at the rate of 147 kW. If we produce it in 1000 sec, we will produce power at the rate of 147 W.

Another useful equation converts current and voltage into power:
P = V A
One Watt = 1 Volt * 1 Amp
A typical alkaline D cell produces about 115 mA at 1.5 V so the power output is 173 mW

Let's look at it this way, 73 Alkaline D cells connected in series would have a voltage of 73 * 1.5 V = 110 V, the same voltage as house current. But the current produced by this battery would still be 115 mA, so the power output would be 73 * 1.5 V * .115 A = 12.6 VA = 12.6 Watts.

When you are billed for electricity, you pay by the kilowatt*hour. That is,
1000 watts * 1 hr * (60 min/hr)*(60 sec/min)*(1 J/watt*sec)*(1 kJ/1000 J)*(1 MJ/1000 kJ)
= 3.6 MJ

Resistance Heating

The voltage across a wire and the current flowing through it are related by Ohm's Law:
V = I R

where Vi is the voltage drop across the wire, I is the current flowing through it, and R is the resistance. The reistance of a wire is related to its length, is diameter, and the material from which it is made. The longer the wire, the higher the resistance. The thinner the wire, the higher its resistance. The unit of resistance is the ohm, which we can understand in terms of unit factors:
( 1 ohm * 1 amp / 1 volt )

Using this new unit factor, we can determine the power dissipated as heat by a wire carrying electrical current:
P = I V
P = I I R
P = I2 R
1 watt = 1 amp2 ohm

When electrical current flows through a wire, it gets hot. The more current that flows, the hotter it gets, and the higher the resistance of the wire, the hotter it gets.

So, we have several new unit factors at our disposal:
(9.8 meter/sec2)
(1 kg meter2/J sec2)
(1 Volt Coulomb/Joule)
(96500 Coulomb/mole e-)
(1 Joule / Watt sec)
(1 Volt Aamp / Watt )
(1 Amp2 Ohm / Watt )

The Electromagnet

The principle device for converting electrical work to mechanical work is the electromagnet. The electromagnet is the basis for all electric motors, relays, solenoids, and transformers. Essentially, an electromagnet is just a coil of wire wound around an iron rod or core. When electrons are forced to move in a circle, they generate a magnetic field. Conversely, when electrons are placed in a magnetic field, they move in a circle. You can build an electromagnet from an iron nail with insulated wire wrapped around it. When you connect your electromagnet to a battery, it will generate a magnetic field that can lift an iron weight, that is, it can convert electrical work to mechanical work.

If the electromagnet is wound around an empty tube, it can actually pull an iron nail into the tube when current is applied. Such a device is called a solenoid:

The wire used to wind an electromagnet must be insulated, i.e. it needs a coating which does not conduct electricity. This insulation might be plastic, rubber, or enamel. At the beginning of the 20th century, silk was used as insulation. Whatever kind of wire is used, the insulation must be stripped from the ends of the wire to make an electrical connection to the battery or switch. While any kind of insulated wire will work in principle, the strength of an electromagnet is proportional to the number of turns in the winding. Therefor, to get the strongest magnet possible, we want to use very fine gauge wire with an enamel coating. This kind of wire is called "magnet wire" because it is used to wind electromagnets and motors. If you buy wire for your project, be sure to specify magnet wire.

Mount a couple of electromagnets on a piece of wood place a piece of steel from a "tin can" above them and you have a primitive telegraph sounder. The metal for the armature must be made of iron or steel. Aluminum and copper are non-magnetic and will not be attracted to the electromagnet.

The Switch

You know what a switch is. You may or may not know how it works. Essentially a switch is just two pieces of metal that can make or break contact. If one of the pieces of metal is iron, we can use an electromagnet to operate the switch. If the switch, in turn, controls the electromagnet, we have a feedback loop that is the heart and soul of all motors.

You can build a simple switch from a tin can or even an aluminum soft drink can. The can will be cut into two strips and bent into the following shapes:

One terminal of the switch is the lever and the other terminal is the bridge. In a simple switch like this one, no magnet is employed and so it does not matter whether the metal used is magnetic.

The Motor

If you combine the switch and the electromagnet into a single circuit, you can build a primitive motor. You will need a cylindrical cork or wood dowell, 8 pins, some magnet wire, 2 magnets, and a battery. Begin by slicing two 1/2 inch thick pieces from the cork to make the bases for the bearings. In each base, stick two pins as shown to make a bearing. The remaining cork will be used for the motor armature. Stick a pin into each end of the cork and adjust them until the cork is perfectly balanced and rides smoothly on the bearings. Now press two more pins into the cork, one on each side of the shaft. These will form you commutator. The shaft should stick out farther than the commutator pins so that the cork can rotate freely. Wind about 10 feet of fine magnet wire around the cork as shown and attach one end of the wire to each of the two commutator pins. You will need to gently scrape the insulation off the ends of the wires to make electrical contact with the commutator pins. Your armature is now complete. Place it on the bearings and make any adjustments to ensure smooth rotation of the armature. Place a magnet one either side of the armature, North on one side and South on the other. Finaly take two wires with the insulation stripped from the ends, attach them to a battery, and touch the ends lightly to the commutator pins. These wires are the brushes for your motor. You must hold them very still as the motor turns.

When the brushes contact the commutator, the circuit is completed and current flows through the armature coil. The magnetic field points perpendicular to the windings, with North on one side and South on the other. The armature will rotate so that the North side of the armature points toward the South pole of the magnet and vice versa. But as the armature turns, the brushes break contact with the commutator pins. As the armature continues to turn, contact between brushes and commutator is reestablished but in the opposite direction: pin 1 now contacts brush 2 and vice versa. With the current now flowing in the direction opposite the original direction, the magnetic field around the armature is reversed. The South pole of the armature now faces the South pole of the magnet and the North pole of the armature faces the North pole of the magnet. The mutual repulsion once again causes the armature to turn until South faces North and the cycle is complete. Thus electrical energy from the battery is converted into circular motion.

Here is a little motor built by Randy Clements in 1997 from 4 corks, 8 pins, about 10 feet of magnet wire, a board and a magnet. Randy discovered that one strong magnet underneath the motor worked almost as well as 2 magnets on either side. It is shown here powered by 4 D cells (6 V).

The Generator

If you think about it, a generator is just a motor operating in reverse. If electrical current can cause a coil of wire to rotate in a magnetic field, rotation of a coil of wire in a magnetic field produces electrical current. The only difference between an AC and a DC generator is the arrangement of the commutator and brushes.

In the DC generator, the commutator makes and breaks in the same manner as the motor shown above. As the armature turns, one brush is always connected to the positive end of the windings and the other is connected to the negative end of the windings. This results in direct current, or DC.

In the AC generator, the commutators never break contact. As one end of the coil winding sweeps past, first the North pole and then the South pole, it changes from positive to negative and back again. The result is alternating current, AC, in which the polarity of the voltage alternates as the armature rotates. If the armature rotates 60 times per second, the frequency of the AC current is 60 cycles per second, or 60 Hertz. In the United States, 60 Hertz is the standard frequency for AC current.

The Transformer

If electricity can be used to produce magnetism, and magnetism can be used to produce electricity, it makes sense to put the two together. In a transformer, two separate coils of wire are wound around an common iron core. One coil, the primary, produces a magnetic field in the core, which in turn generates and electrical current in the secondary coil. The ratio of the number of turns in the primary to that in the secondary, determines the relative voltages and currents in the two coils. No energy is lost in principle: product V*A is constant. Thus in a step-up transformer, low voltage-high current electricity is transformed to high voltage-low current electricity. The transformer only works for AC electricity, however, since there is no mechanical commutator as there is in the DC motor/generator.


In 1879, Edison and Swan independently invented the modern electric incandescent lamp and this invention started the race for the electrification of the world. In 1880, Edison built an electrical power plant in London and in 1882 built the Pearl Street station in New York City. Edison provided high current, low voltage, DC electrical power using DC generators powered by steam engines. This form of electricity was compatible with electrical devices which had been powered by batteries from the beginning of the 19th Century. Most important of these was the electric motor.

Nicola Tesla emigrated from Croatia to the United States, working briefly for Edison. Telsa realized that since transmission losses in wires increase with the amount of current, high-voltage, low current transmission lines would be more efficient for carrying electricity from central power generation facilities to industrial and domestic users. AC is easily converted back and forth between high voltage and low voltage using the transformer (which does not work for DC current). Consequently, Tesla advocated AC as the standard for electrical power generation. Edison disagreed with Tesla and the two parted company. In 1884, Tesla invented the AC generator.

We can understand the advantages of AC over DC in the following terms. Consider a power station generating 1000 Watts of power and the transmission line with a resistance of 1 Ohm. What voltage should the power station use to maximize its efficiency? Lets consider three voltages, 50 V, 100 V and 1000 V.
50 V100 V1000 V
Generator Power1000 Watt1000 Watt1000 Watt
Current1000 Watt/ 50 V)(1000 Watt/ 100 V)(1000 Watt/ 1000 V)
20 Amp10 Amp1 Amp
Transmission line loss(20 Amp)2 1 Ohm(10 Amp)2 1 Ohm(1 Amp)2 1 Ohm
400 Watt100 Watt1 Watt
Available Power(1000-400) Watt(1000-100) Watt(1000-1) Watt
600 Watt900 Watt999 Watt

In all three systems, the generator is putting out 1000 Watts. With the transmission line at 1000 V, 999 Watts are available to the user. But at 50 V, only 600 Watts are available to the user and 400 Watts are wasted in heating the transmission line. The higher the voltage of the transmission line, the more efficient the distribution of electricity. The problem is, we don't want high voltages at the user end, since this requires more insulation for the conductors in wiring and appliances.

With AC electricity, the transformer provides a very efficient means of changing high voltage to low voltage and back again. So the generator can produce modest voltages, this can be stepped up to high voltage to minimize transmission losses, and then stepped back down again before it enters the home or business. With an AC distribution system, you can build one big power plant to serve a large area.

With DC electricity, there is no such possibility. A transformer works only for AC and no efficient means of stepping DC electricity up and down has yet been devised. The only alternative for DC power distribution is to minimize transmission losses by minimizing the length of the tranmission lines. This means that you have to build many small power plants close to the end users. This was Edison's vision for the future of electrification.

So in 1884 the situation is this: DC can be generated in local power plants, sent over short transmission lines, and used to power electric lights and motors. AC can be generated in central power plants, sent long distances, and used to power electric lights only. As long as there was no AC motor, the DC plan seemed the most beneficial.

Tesla's patents were quickly purchased by Edison's rival, George Westinghouse, and a bitter power struggle (pun intended) began over the future of electrical power generation, the so called "current war." In 1888, Tesla invented the AC motor, closing a gap in the relative practicality of AC and DC electricity. Edison did his best to demonstrate that AC electricity was unsafe. In 1890, he lobbied to have the first electric chair wired with AC electricity. In 1891, Tesla invented the Tesla Coil, a device for producing extremely high voltages at tiny currents and toured the country demonstrating the safety of AC by allowing high voltages to flow through his body, lighting lamps he held in his hands.

In 1893, Westingouse lighted the Columbian Exposition in Chicago, demonstrating the practicality of large-scale electrical production. In 1896, he built a power plant at Niagara Falls and used it to provide power to Buffalo. From this point on, Edison's DC power plants were at a terrible disadvantage because of their encumbant transmission losses and AC power emerged as the dominant form of power generation. Today, electrical power plants are centralized and sent their power over long, high voltage transmission lines. You can see the transformers used to step this high voltage down to low voltage. Just look for the large metal cylinders, affectionately called "pole pigs," where the power line enters a residence or business.

At Virginia Power, for example, electrical power is stepped up from the generator to 230,000 Volts for distribution over the grid. As the lines get into communities, the voltage is stepped down to lower voltages, 115,000 V,

Electromechanical Links

The Electrical Power Quiz


You will design and build a simple electromechanical device employing both a switch and an electromagnet. You may choose to build:

If your device moves when connected to a battery, you pass. If not, you fail.

This little motor was built by Haden Hopkins in 1998. A single permanent magnet is placed below the motor.

Here is a close-up of the commutator. One end of the magnet wire winding is soldered to each of the commutator poles.

Here it is in operation. One battery lead is held next to each pole of the commutator.