Electrical Safety Codes For safety reasons, electrical codes...

Electrical Safety Codes For safety reasons, electrical codes have been established that limit the amount of current a wire of a given size can carry. For example, an 18 -gauge (crosssectional area $=1.17 \mathrm{mm}^{2}$ ), rubber-insulated extension cord with copper wires can carry a maximum current of $5.0 \mathrm{A}$. Find the voltage drop in a 12 -ft, 18 -gauge extension cord carrying a current of $5.0 \mathrm{A}$. (Note: In an extension cord, the current must flow through two lengths - down and back.)

Key Concepts

Ohm's Law

Ohm's Law is the fundamental principle that defines the relationship between voltage, current, and resistance in an electrical circuit. It states that the voltage drop across a conductor is equal to the current passing through it multiplied by the resistance of the conductor, which is key in calculating voltage drop in any electrical system.

Resistance of a Conductor

The resistance of a conductor is determined by its physical properties and dimensions. It is calculated using the formula R = (?L)/A, where ? is the material’s resistivity, L is the length of the conductor, and A is its cross?sectional area. This principle is crucial for understanding how variations in a wire's length and area affect its resistance.

Wire Gauge and Cross?Sectional Area

Wire gauge is a measure of the diameter of a wire, which directly relates to its cross-sectional area and its current-carrying capacity. A smaller gauge number corresponds to a thicker wire with lower resistance, while a higher gauge number indicates a thinner wire with higher resistance, which is an essential consideration in designing safe and efficient electrical circuits.

Circuit Path Length in Extension Cords

In circuits such as extension cords, the total effective length over which the current flows includes both the outgoing and return paths. This means that the calculated resistance—and consequently the voltage drop—must account for the entire path through which the current travels, effectively doubling the length of conductor considered in the resistance calculation.

Resistivity and Material Properties

Resistivity is an intrinsic property of materials that indicates how strongly a material opposes the flow of electric current. Different materials have different resistivities, and for conductors like copper, a low resistivity allows efficient current flow while still contributing to a voltage drop over long distances, making it a key concept in practical electrical designs.

Transcript

00:02 Let's consider the cross -sectional area of a wire of a certain length not drawn to scale just done like that so it's easier to perceive so we are given the cross -sectional area one seven meters squared the length is equal to 12 feet the length of this wire there's a current traveling through this wire at 5 .0 ampiers the resistivity this is not given in the question however, if you look it up in a table in the back of your book, you should find that the resistivity of copper is 1 .68 times 10 to the negative 8 meters.

01:08 By convention, we're given resistivity in that particular set of units, but we need to consider both cross -sectional area and length.

01:18 So to do this, we take our resistivity times length over area.

01:28 I just think about the units here.

01:30 Length is in meter units.

01:32 A is in area, is a meter squared resistivity.

01:38 That is in ome meters.

01:43 So units cancel out for meters, but you'll be lucky with oms.

01:50 Now, if we know that, let's go ahead and rewrite.

01:56 Resistance over here.

02:01 If you know that this is the resistance, we are given the current equals 5 .0 ampers.

02:11 Now what kind of information do we want to find with all this nonsense? and the answer is we want the voltage drop, which is just another way of saying the change in voltage across this wire.

02:25 So i presume you recall a lot.

02:31 So we have r and i.

02:39 I realize that.

02:40 But we'll solve it.

02:45 Here we go...

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