iot poly engineering 4-04 drill april 30, 2009 the power loss in a transmission cable is given by...

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POLY ENGINEERING4-04

DRILL April 30, 2009

The power loss in a transmission cable is given by the equation P= I2R.

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?

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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 4I2.

The new power is P=4I2R, which is FOUR times theoriginal power loss.

Let’s look at a simple example ……

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Given: The resistance of a power line is 10 ohms, and the current is 10 amperes.

P = I2RP = (10 A)2(10 ohms)P = 100 A2 (10 ohms)P = 1000 Watts

Now, we double the current, while keeping the same resistance.

P= I2RP= (20 A)2(10 ohms)P= 400 A2(10 ohms)P= 4000 Watts

Conclusion: If the current is doubled, while the resistance is held constant, the power loss will be quadrupled.

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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 0.25I2.

The new power is P=.25I2R, which is ONE-FOURTH times theoriginal power loss.


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Given: The resistance of a power line is 10 ohms, and the current is 10 amperes.

P = I2RP = (10 A)2(10 ohms)P = 100 A2 (10 ohms)P = 1000 Watts

Now, we halve the current, while keeping the same resistance.

P= I2RP= (5 A)2(10 ohms)P= 25 A2(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.

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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:

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All metal wires have resistance. The resistance of a wire is based on 4 factors:1. Material2. Length3. Cross-sectional area4. Temperature

Let’s review what we learned yesterday about the resistance of a wire:

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1. 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 barsCopper wire

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2. Length:A long wire will have more resistancethan 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 theindividual resistors.

RT= R1 + R2 + … + Rn

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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.

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3. 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 theindividual resistors.

RT= R1 + R2 + … + Rn1 1 1 1

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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 bulbis very thin, thus giving it a high resistance which causesit to get hot and glow. The same thing occurs in anelectric toaster, where the wire becomes red hot.

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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.

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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.

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When two or more resistors are connected in series, their combined resistance is greater than any of theindividual resistors.

RT= R1 + R2 + … + Rn

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?

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RT= R1 + R2 + … + Rn

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 = 2200brown-black-red = 1000yellow-violet-orange = 47000

RT= R1 + R2 + … + Rn = 2200 + 1000 + 47000RT = 50200 ohms

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When two or more resistors are connected in parallel, their combined resistance is less than any of theindividual resistors.

RT= R1 + R2 + … + Rn1 1 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?

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RT= R1 + R2 + … + Rn1 1 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 = 3000red-black-red = 2000blue-black-red = 6000

1 1 1 1RT= R1 + R2 + … + Rn

= 3000 + 2000 + 6000 = 6000 + 6000 + 6000

= 6000 = 1000

1 1 1

2 3 1

6 1RT = 1000 ohms

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How would you find the equivalent resistance of the following combination?

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HOMEWORK: Study for a quiz on Electricity/Electronics tomorrow.

iot poly engineering 4-04 drill april 30, 2009 the power loss in a transmission cable is given by...

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