Math

QuestionWhat are three ways you could decrease the resistance of a wire?

Studdy Solution

STEP 1

What is this asking? How can we make a wire less resistant to electrical current flow?
Think of it like making a water slide slipperier! Watch out! Don't mix up resistance with resistivity.
Resistivity is a property of the *material* the wire is made of, while resistance is a property of the *wire itself*.

STEP 2

1. Material
2. Length
3. Thickness

STEP 3

We can **decrease** the resistance of a wire by choosing a material with *lower* **resistivity**.
Think of copper versus rubber.
Copper has *much* lower resistivity, so it's used in wires!
It's like choosing a material for our water slide that's naturally slicker.

STEP 4

We can **decrease** the resistance of a wire by making it *shorter*.
Imagine trying to push water down a *really* long slide versus a short one.
The shorter slide offers less resistance.
The same is true for wires and electrons!
A shorter wire means less resistance to the flow of charge.

STEP 5

Mathematically, the resistance RR of a wire is *directly* proportional to its length LL: RL R \propto L This means if we *halve* the length, we *halve* the resistance!

STEP 6

We can **decrease** the resistance of a wire by making it *thicker*.
A thicker wire is like a wider water slide.
It gives more room for the electrons to flow, just like a wider slide gives more room for the water.

STEP 7

Mathematically, the resistance RR of a wire is *inversely* proportional to its cross-sectional area AA: R1A R \propto \frac{1}{A} This means if we *double* the area, we *halve* the resistance!
If we *quadruple* the area, we reduce the resistance to a *quarter* of its original value!

STEP 8

Three ways to decrease the resistance of a wire are: 1.
Use a material with **lower resistivity**, 2.
Make the wire **shorter**, and 3.
Make the wire **thicker** (larger cross-sectional area).

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