IOT POLY ENGINEERING 4-04 DRILL April 30, 2009 The power loss in a transmission cable is given by the equation P= I 2 R. A.If the original current is doubled, while the resistance remains constant, what will happen to the power loss? B.If the original current is cut in half, while the resistance remains constant, what will happen to the power loss?

IOT POLY ENGINEERING 4-04 The power loss in a transmission cable is given by the equation P= I 2 R. A.If the original current is doubled, while the resistance remains constant, what will happen to the power loss? When current is doubled, the new current is 2 I. In the power equation, we must square current. Therefore, we square 2 I, which becomes 2Ix2I or 4I 2. The new power is P=4I 2 R, which is FOUR times the original power loss. Let’s look at a simple example ……

IOT POLY ENGINEERING 4-04 Let’s look at a simple example …… Given: The resistance of a power line is 10 ohms, and the current is 10 amperes. P = I 2 R P = (10 A) 2 (10 ohms) P = 100 A 2 (10 ohms) P = 1000 Watts Now, we double the current, while keeping the same resistance. P= I 2 R P= (20 A) 2 (10 ohms) P= 400 A 2 (10 ohms) P= 4000 Watts Conclusion: If the current is doubled, while the resistance is held constant, the power loss will be quadrupled.

IOT POLY ENGINEERING 4-04 The power loss in a transmission cable is given by the equation P= I 2 R. B.If the original current is cut in half, while the resistance remains constant, what will happen to the power loss? When current is halved, the new current is 0.5 I. In the power equation, we must square current. Therefore, we square 0.5 I, which becomes 0.5Ix0.5I or 0.25I 2. The new power is P=.25I 2 R, which is ONE-FOURTH times the original power loss. Let’s look at a simple example ……

IOT POLY ENGINEERING 4-04 Let’s look at a simple example …… Given: The resistance of a power line is 10 ohms, and the current is 10 amperes. P = I 2 R P = (10 A) 2 (10 ohms) P = 100 A 2 (10 ohms) P = 1000 Watts Now, we halve the current, while keeping the same resistance. P= I 2 R P= (5 A) 2 (10 ohms) P= 25 A 2 (10 ohms) P= 250 Watts Conclusion: If the current is halved, while the resistance is held constant, the power loss will be one-fourth of the original value.

IOT POLY ENGINEERING 4-03 There are six ways to generate (create) electricity: 1. Friction 2. Chemical 3. Light 4. Heat 5. Pressure 6. Magnetism Let’s review what we learned yesterday about the sources of electricity:

IOT POLY ENGINEERING 4-04 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 Let’s review what we learned yesterday about the resistance of a wire:

IOT POLY ENGINEERING Material: Some materials conduct electricity better than other materials. For example, gold conducts electricity better than silver, which conducts electricity better than copper. However, gold and silver are extremely expensive compared to copper, so they are only used in very special cases. Material technology (one of the 9 Core technologies) is very important in Electricity and Electronics. Gold bars Silver bars Copper wire

IOT POLY ENGINEERING Length: A long wire will have more resistance than a shorter wire of the same material, cross-sectional area, and temperature. When two or more resistors are connected in series, their combined resistance is greater than any of the individual resistors. R T = R 1 + R 2 + … + R n

IOT POLY ENGINEERING 4-04 Imagine that a long wire is simply two shorter wires connected end-to-end in series. 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.

IOT POLY ENGINEERING Cross-sectional Area: A thick wire will have less resistance than a thin wire of the same material, length, and temperature. When two or more resistors are connected in parallel, their combined resistance is less than any of the individual resistors. R T = R 1 + R 2 + … + R n 1 1

IOT POLY ENGINEERING 4-04 Imagine that a thick wire is simply two or more wires bundled together side-by-side in parallel. 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.

IOT POLY ENGINEERING 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.

IOT POLY ENGINEERING 4-04 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.

IOT POLY ENGINEERING 4-04 When two or more resistors are connected in series, their combined resistance is greater than any of the individual resistors. R T = R 1 + R 2 + … + R n Solve the following: A red-red-red resistor, a brown-black-red resistor, and a yellow-violet-orange resistor are connected in series. What is the resistance of this combination?

IOT POLY ENGINEERING 4-04 R T = R 1 + R 2 + … + R n Solve the following: A red-red-red resistor, a brown-black-red resistor, and a yellow-violet-orange resistor are connected in series. What is the resistance of this combination? red-red-red = 2200 brown-black-red = 1000 yellow-violet-orange = R T = R 1 + R 2 + … + R n = R T = ohms

IOT POLY ENGINEERING 4-04 When two or more resistors are connected in parallel, their combined resistance is less than any of the individual resistors. R T = R 1 + R 2 + … + R n 1 1 Solve the following: An orange-black-red resistor, a red-black-red resistor, and a blue-black-red resistor are connected in parallel. What is the resistance of this combination?

IOT POLY ENGINEERING 4-04 R T = R 1 + R 2 + … + R n 1 1 Solve the following: An orange-black-red resistor, a red-black-red resistor, and a blue-black-red resistor are connected in parallel. What is the resistance of this combination? orange-black-red = 3000 red-black-red = 2000 blue-black-red = R T = R 1 + R 2 + … + R n = = = 6000 = R T = 1000 ohms

IOT POLY ENGINEERING 4-04 How would you find the equivalent resistance of the following combination?

IOT POLY ENGINEERING 4-04 HOMEWORK: Study for a quiz on Electricity/Electronics tomorrow.