An 8.00- ft extension cord has two 18 -gauge copper wires, each having a diameter of 1.024 mm. A

step 1 Okay, so we know that we have an extension card that has two wires. So the length they give us i

An 8.00- ft extension cord has two 18 -gauge copper wires,...

Key Concepts

Geometric Calculation of Cross?Sectional Area

The cross?sectional area of a conductor, particularly one with a circular cross section, is calculated using the formula A = ?(d/2)², where d is the diameter of the wire. This geometric concept is crucial since the area directly influences the resistance of the conductor; a larger area results in lower resistance, while a smaller area increases resistance.

Resistance Calculation

Calculating the resistance of a uniform conductor involves using the relation R = ?L/A. Here, L is the length of the conductor and A is its cross-sectional area. In circuits, knowing how to calculate resistance from these physical dimensions and material properties is essential for predicting the behavior of current and voltage drop across components such as wires or cables.

Resistivity

Resistivity is an intrinsic property of a material that quantifies how strongly it opposes the flow of electric current. It is used to determine the resistance of a conductor through the relationship R = ?L/A, where ? is the resistivity, L is the conductive length, and A is the cross?sectional area. This concept is fundamental in material science and electrical engineering when analyzing how different materials behave in electrical circuits.

Electrical Power Dissipation

Electrical power dissipation in a resistor, often referred to as Joule heating, is given by the formula P = I²R, where I is the current through the resistor. This concept explains how electrical energy is converted into heat in any resistive element and is a key consideration in circuit design to prevent overheating and ensure proper energy management.

Transcript

00:01 Okay, so we know that we have an extension card that has two wires.

00:09 So the length they give us is 8 foot, but since we have 2 is 16 foot, and i already converted these to the 6 meters, okay? and we know the diameter or the gouge of the wire.

00:28 And we want to know at what rate is energy delivered for two different values of the current.

00:35 Okay, so normally, we know that power, okay, that is energy delivered per unit of time equals the current squared times the value of the resistance.

00:52 Okay, but you can see we do not have the resistance, okay, but we know that the, uh, the, resistance particularly for a wire can be calculated as the resistivity okay this is a a fantasy let's say it's unique for each material okay it says us how hard is for electrons to pass through this material okay so resistivity since we have a copper i already put here the value of the resistivity of copper okay times the length of the wire and all of this divided by the area of the wire the transversal area okay so i have my wire here this is the left okay and this of this and this part is the the area i'm looking okay and the resistivity is just of the material okay obviously it's not the same for metals than for another kind of stuff okay and so what i have to do it's actually remember that an area remember we assume this is a circle okay so the area of the circle equals p times the radio square okay so that is why i have the diameter so the half of the diameter is the radio and i then have all the things i need to calculate this okay so the first part it will be for the 1 ampere okay so i will have that power equals 1 amp squared you see there is the problem here times the resistivity okay that is uh 1 .7 times 10 to the minus 8 um per meter okay times uh all this multiply it by the length that is uh 4 .87 meters okay you see now what is important to have these meters and divided of the by pi times the radio 0.

03:03 Okay, remember we have millimeters here, so we need actually just a meter...

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