1. IOT POLY ENGINEERING 4-03 DRILL April 29, 2009 Ohm’s Law states that voltage equals current times resistance, V=IR. Watt’s Law states that power equals voltage times current, P=VI. Watt’s Law is most useful when the voltage and current are given, but sometimes they are not known. Derive 2 more equations for Power. One equation should involve only voltage and resistance. The second equation should involve only current and resistance.

2. IOT POLY ENGINEERING 4-03 1. Start with Ohm’s Law: V=IR 3. State Watt’s Law: P=VI Derivation #1 – voltage and resistance only 2. Divide both sides by R: V/R=I 4. Substitute V/R for I: P=V(V/R) 5. Combine like terms: P=V 2 /R

3. IOT POLY ENGINEERING 4-03 1. Start with Ohm’s Law: V=IR 2. State Watt’s Law: P=VI Derivation #2 – current and resistance only 3. Substitute IR for V: P=(IR)I 4. Combine like terms: P=I 2 R Let’s check our two derived equations by re-solving yesterday’s drill questions.

4. IOT POLY ENGINEERING 4-03 Solve the following problems. Draw a schematic diagram and label all electrical components. Show all equations, substitutions, and box in your answers with units. 1. What is the power when 12 amperes flow through a 15 ohm resistor? 15 W 12 A P=I 2 R P= (12 A) 2 (15 W ) P= 2160 Watts P= (144 A 2 )(15 W ) This is the same answer we got yesterday by another method!

5. IOT POLY ENGINEERING 4-03 Solve the following problems. Draw a schematic diagram and label all electrical components. Show all equations, substitutions, and box in your answers with units. 2. What is the power when a 9 Volt battery is connected to a 0.3 ohm resistor? 0.3 W 9 V P=V 2 /R P= (9 V) 2 /(0.3 W ) P= 270 Watts P= (81 V 2 )/(0.3 W ) This is the same answer we got yesterday by another method!

6. IOT POLY ENGINEERING 4-03 There are six ways to generate (create) electricity: 1. Friction - Rubbing two objects together can remove electron(s) from some neutral atoms, and deposit the electron(s) on other neutral atoms. The atoms that lose electrons become positively charged, while the atoms that gain electrons become negatively charged. This type of electricity is called 'static' electricity, because it is not moving, but is stationary.

7. IOT POLY ENGINEERING 4-03 One example of static electricity in nature is the accumulation of charges on clouds, which eventually results in lightning as the large static charge discharges into the ground. Friction is not a practical method of creating electricity for use in modern electrical devices such as TV, radio, refrigerators, etc.

8. IOT POLY ENGINEERING 4-03 2. Chemical - Electricity can be produced by placing two dissimilar metals in a liquid called an electrolyte. For example, if zinc (Zn) and copper (Cu) are placed in salt water, electricity can be produced. Some examples of chemical cells: car batteries, AA batteries, AAA batteries, hearing aid batteries, flashlight batteries, etc.

9. IOT POLY ENGINEERING 4-03 3. Light - Electricity can be produced by using special devices called photocells, which convert light into electrical energy. Photocells are found in devices like 'solar' calculators, which use light to create electricity. Solar panels are becoming very popular as a way of producing large amounts of electricity. Photocells should not be confused with photoresistors. Photoresistors do not create electricity, they merely change resistance when exposed to light.

10. IOT POLY ENGINEERING 4-03 4. Heat - Electricity can be produced by using special devices called thermocouples, which convert heat into electrical energy. The thermocouple is made of two dissimilar metals, joined at a junction. Thermocouples are often used in control systems. For example, the thermocouple can be used to turn a device on or off depending on the temperature.

11. IOT POLY ENGINEERING 4-03 5. Pressure - Electricity can be produced by using special devices called piezoelectric cells, which convert pressure into electrical energy. Piezoelectric cells are often found in tiny microphones and earphones. In a microphone, a piezoelectric cell converts sound pressure into electrical current. In an earphone, a piezoelectric cell converts electrical current into sound. What very common modern device utilizes a tiny microphone and earphone?

12. IOT POLY ENGINEERING 4-03 6. Magnetism - Electricity can be produced by moving a magnet past a wire (or vice versa), which converts motion (kinetic energy) into electrical energy. This method is the most practical way of generating electricity in large amounts. In order to make the magnet move past the wire (or vice versa), we can utilize a turbine to turn the generator. In our IOT unit on Power and Energy, we saw turbine-generator combinations used in hydroelectric plants, wind turbine power plants, nuclear power plants, coal-fired steam cycle power plants.

13. IOT POLY ENGINEERING 4-03 All metal Wires have resistance. The resistance of a wire is based on 4 factors: 1. Material 2. Length 3. Cross-sectional area 4. Temperature

14. IOT POLY ENGINEERING 4-03 1. Material: Some materials conduct electricity better than other materials. For example, gold conducts electricity better than copper. However, gold is extremely expensive compared to copper, so it is only used in very special cases. Material technology (one of the 9 Core technologies) is very important in Electricity and Electronics.

15. IOT POLY ENGINEERING 4-03 2. Length: A long wire will have more resistance than a shorter wire of the same material, cross-sectional area, and temperature. Imagine that a long wire is simply two shorter wires connected end-to-end in series. When two or more resistors are connected in series, their combined resistance is greater than any of the individual resistors. Therefore, a long wire has a resistance which is the sum of the resistances of the shorter pieces. One of the reasons for the development of modern micro-circuits is to reduce the resistance, thus causing the power requirements to be minimized.

16. IOT POLY ENGINEERING 4-03 3. Cross-sectional Area: A thick wire will have less resistance than a thin wire of the same material, length, and temperature. Imagine that a thick wire is simply two or more wires bundled together side-by-side in parallel. When two or more resistors are connected in parallel, their combined resistance is less than any of the individual resistors. Therefore, a thick wire has a resistance which is less than the resistances of the thinner pieces. You have probably noticed that the wire in a light bulb is very thin, thus giving it a high resistance which causes it to get hot and glow. The same thing occurs in an electric toaster, where the wire becomes red hot.

17. IOT POLY ENGINEERING 4-03 4. Temperature: In general, as the temperature of a wire increases, the resistance increases. The opposite is true as well. As the temperature of a wire decreases, the resistance decreases. The changes of resistance with temperature can be explained by looking at the Chemistry involved. When a metal is heated, the molecules move farther apart and move faster. Therefore, for electrons to jump from one atom to another (electrical current) in a heated metal, they must move farther, and they must hit a 'moving target' (the next atom). This makes it more difficult for electrons to move, thus increasing the resistance.

18. IOT POLY ENGINEERING 4-03 Conversely, when a metal is cooled, the molecules move closer together, and become less active. Therefore, for electrons to jump from one atom to another (electrical current) in a cooled metal, they do not have to move as far, and they can easily hit a more stationary target (the next atom). This makes it easier for electrons to move, thus lowering the resistance. Modern engineers and scientists are developing low-temperature superconductors so that electrical power requirements can be minimized.