Mengapa ketebalan kawat mempengaruhi resistansi?

15

Seorang guru menjelaskan mengapa dengan menggunakan analogi jalan raya. Semakin banyak jalur yang Anda miliki, semakin cepat mobil melaju, di mana jumlah jalur jelas mewakili ketebalan kawat dan mobil mewakili elektron. Cukup mudah.

Tetapi setelah titik tertentu bukankah seharusnya kawat menjadi terlalu tebal, sehingga ketebalan setelah itu tidak mempengaruhi resistansi? Misalnya, jika Anda memiliki 100 mobil di jalan raya, jalan raya 4 lajur akan memungkinkan mobil bergerak lebih cepat daripada lajur 1, karena ada lebih sedikit mobil per lajur. Tetapi jalan raya 1000 lajur akan seefisien 10.000 lajur, karena di kedua jalan raya setiap mobil memiliki lajur sendiri. Setelah 100 lajur, jumlah lajur tidak memberikan perlawanan.

Jadi mengapa peningkatan ketebalan kawat selalu mengurangi resistensi?

pengguna27379
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11
Jangan memikirkan jalan raya 100 lajur dengan 100 mobil vs. jalan raya lajur 100 dengan 100 mobil, alih-alih menganggapnya sebagai jalan raya 100 lajur dengan satu triliun mobil vs. jalan raya lajur 10000 dengan satu triliun mobil (atau apa pun yang sangat besar jumlah mobil yang Anda inginkan).
helloworld922
@ helloworld922 Tapi poin saya masih berlaku. Satu triliun mobil yang berjalan di 10 triliun lajur sama cepatnya dengan satu triliun mobil yang berjalan di lajur 100 Triliun.
user27379
3
@ user27379 Tapi selalu ada lebih banyak mobil daripada jalur.
Penguin Anonim
Bukan ahli, tetapi jika kabelnya cukup tebal, bukankah itu akan mulai berperilaku lebih seperti kapasitor daripada resistor?
Alistair Buxton
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Ada lebih banyak area permukaan pada kawat tebal untuk melakukan perjalanan elektronik, yang berarti Anda akan memiliki lebih banyak elektron yang bepergian melalui kabel tebal daripada kabel tipis.
Charles Addis

Jawaban:

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Analogi mobil itu tidak begitu bagus, karena elektron tidak benar-benar mengalir dari satu ujung kawat ke ujung lainnya (baik mereka lakukan tetapi sangat lambat) dan itu menyiratkan ada beberapa ruang antara mobil, sedangkan itu akan menjadi lebih seperti kemacetan apa pun selebar jalan raya.
Ini lebih seperti garis bola biliar, dan gaya diterapkan pada yang pertama, dan energinya ditransfer ke yang terakhir melalui semua bola perantara (sedikit seperti ayunan newton, meskipun bola tidak benar-benar memantul satu sama lain ). Elektron bebas memantul, kadang-kadang terhambat (lihat di bawah) dengan perbedaan potensial yang menyebabkan kecenderungan rata-rata ke arah arus.

Analogi air lebih baik - pipa selalu penuh air, dan untuk pompa (baterai) yang sama, tekanan (tegangan) selalu lebih rendah semakin lebar pipa, yang menyamakan lebih banyak aliran dan hambatan yang lebih rendah.

Kutipan dari halaman Wiki tentang resistivitas ini menjelaskan dengan cukup baik:

Dalam logam - Sebuah logam terdiri dari kisi-kisi atom, masing-masing dengan kulit terluar elektron yang lepas dari atom induknya dan bergerak melalui kisi. Ini juga dikenal sebagai kisi ionik positif. 4 Dekat suhu kamar, logam memiliki ketahanan. Penyebab utama resistensi ini adalah gerakan termal dari ion. Ini bertindak untuk menyebarkan elektron (karena gangguan destruktif dari gelombang elektron bebas pada potensi ion yang tidak berkorelasi) [rujukan?]. Juga berkontribusi terhadap resistensi pada logam dengan kotoran adalah ketidaksempurnaan yang dihasilkan dalam kisi. Dalam logam murni sumber ini dapat diabaikan [rujukan?]
'Lautan' elektron yang tidak dapat dipisahkan ini memungkinkan logam mengalirkan arus listrik. Ketika perbedaan potensial listrik (tegangan) diterapkan pada logam, medan listrik yang dihasilkan menyebabkan elektron bergerak dari satu ujung konduktor ke ujung lainnya.

Semakin besar luas penampang konduktor, semakin banyak elektron per satuan panjang yang tersedia untuk membawa arus. Akibatnya, resistansi lebih rendah pada konduktor penampang yang lebih besar. Jumlah peristiwa hamburan yang ditemui oleh elektron yang melewati suatu material sebanding dengan panjang konduktor. Semakin lama konduktor, semakin tinggi resistansi. Bahan yang berbeda juga memengaruhi resistensi.

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Oli Glaser
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Tetapi bahkan dengan menggunakan analogi air, poin saya masih tetap. Seember air yang dituangkan melalui terowongan akan menghadapi jumlah resistensi yang sama tidak peduli berapa ukuran terowongan itu!
user27379
2
Itulah intinya - akan ada udara di dalam terowongan, sedangkan kawat selalu benar-benar "penuh". Ini sama dengan air dalam ember yang membentuk film yang sangat tipis untuk menutupi diameter terowongan, jika Anda mengerti maksud saya.
Oli Glaser
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Anda tidak hanya "menuangkan elektron" ke salah satu ujung kabel - mereka sudah ada di sana.
Oli Glaser
Maaf, sulit untuk menemukan analogi yang sangat bagus - mereka semua memiliki ketidakakuratan. Saya menambahkan kutipan dan tautan ke halaman Wiki tentang resistensi, jika Anda membaca ini dengan seksama Anda harus mendapatkan ide yang bagus tentang fisika. Omong-omong, situs fisika lain dan tumpukan fisika akan menjadi tempat yang baik untuk penelitian / bertanya.
Oli Glaser
Saya tidak tahu apakah itu masalahnya tetapi, dengan AC "efek kulit" juga mengurangi penampang kabel yang efektif.
キ キ ジ キ
7

Saya akan mendekati pertanyaan Anda dengan cara yang sedikit berbeda untuk mencoba dan memberi Anda pemahaman yang sedikit lebih intuitif tentang mengapa resistensi turun.

Pertama mari kita pertimbangkan resistensi setara dari rangkaian sederhana:


(sumber: electronics.dit.ie )

1RTotal=1R1+1R2+1R3...1Rn

Anda dapat melihat persamaan ini di buku teks, tetapi Anda mungkin bertanya-tanya, "Tapi Anda menambahkan lebih banyak resistor! Bagaimana itu bisa membuat resistensi turun?".

G=1RGR

Sekarang bagian ini menarik, lihat apa yang terjadi ketika kita menggunakan konduktansi dalam persamaan resistansi rangkaian paralel.

Conductance=GTotal=G1+G2+G3..Gn=1RTotal=1R1+1R2+1R3...1Rn

We see here that conductance increases as you add more resistors in parallel, and resistance decreases! Each resistor is able to conduct a certain amount of current. When you add a resistor in parallel, you are adding an additional path through which current can flow, and each resistor contributes a certain amount of conductance.

When you have a thicker wire, it effectively acts like this parallel circuit. Imagine you have a single strand of wire. It has a certain conductance and a certain resistance. Now imagine you have a wire that is composed of 20 individual strands of wire, and each strand is as thick as your previous single strand.

If each strand has a certain conductance, having a wire with 20 strands means that your conductance is now 20 times larger than the wire with only 1 strand. I'm using strands because it helps you see how a thicker wire is the same as having multiple smaller wires. Since the conductance increases, it means the resistance decreases (since it is the inverse of conductance).

Scott Lawson
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2

Forget the highway analogy. The resistance of a wire depends on 3 parameters: the conductivity of the material from which the wire is made, its cross sectional area, and its length. Highly conductive materials, such as copper and silver, are used to manufacture wire to achieve a low resistance. The longer a wire is the more resistance it has due to the longer path the electrons have to flow along to get from one end to the other. The larger the cross sectional area, the lower the resistance since the electrons have a larger area to flow through. This will continue to apply no matter how thick the wire is. The electron flow will adjust itself to whatever the wire thickness is.

Barry
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2
Still doesn't answer "why does the electron flow adjust to wire thickness beyond a certain point" though.
us2012
You didn't answer the question, you just rephrased what I already know! Why do the electrons adjust themselves?
user27379
I'm sure Barry knows, but for others, please note that "the conductivity of the material" is itself dependent on many factors (temperature, purity, pressure, etc...)
DrFriedParts
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Electricity is nothing but the flow of electrons through a material. In one way, it's like a garden hose already full of water. When the water turned on (pressure applied) at the faucet, the pressure travels through the hose much faster than any particular water molecule, and water begins flowing out of the far end nearly immediately. A wire is chock full of electrons able to move when you apply a bit of electromotive force. Apply a voltage, and you don't have to wait for the first electrons in to traverse the wire, they start moving at the far end almost immediately.

Now think of a cross section of the wire . . . imagine drawing a line around the wire, perpendicular to the axis of the wire. Now imagine counting the number of electrons passing this line, through the circle that is the cross section of the wire. This is the current, measured in amps. There are a couple of ways you can have the same current. Lots of electrons drifting slowly by, or fewer electrons hauling a&& to get the same number passing through your cross section per second, and hence the same current.

How do you convince them to move faster? Apply a greater electromotive force. So in a wire with half the diameter, you'd have one fourth the cross-sectional area, which means one fourth the number of electrons available in any given length of wire to pass your line per second. What'cha gonna do to get that current up with fewer electrons available to move? You're gonna have to move them faster so that the same number can pass by per second by applying a higher voltage.

There you have it: A thinner wire requires a higher voltage to carry the same current. That's pretty much the definition of resistance, since V/I = R.

Marc
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Do you know why doesn't the car analogy works fine? Even if we disregarded the possibility that electrons don't really actually move, you'd thing about them again as cars but not moving in straight lines! They move in a random zig zag paths. Therefore; the more lines the less possibility the cars will ever collide even with a zig zag path.

So you tacitly assumed electrons move in staright lanes (lines) just like cars, which in that case your assumption that the thickness of the wire won't affect. On the other hand, considering the cars to move in a non-straight lines, your assumed hypothesis won't fit your conclusion.

Adel Bibi
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There are still a lot of problems with this explanation: (1) cars moving in zig-zag paths across lanes are no longer an intuitive "cars on a highway" analogy, (2) for the most part, electrons collide with the metal lattice (the "road" in the analogy) not other electrons ("cars") and that doesn't change much with a wider wire/road, (3) You still have to explain why "less possibility of collision" results in more flow (remember collisions are almost completely elastic). The electrons colliding simply means more zig-zagging, not reduced speed.
DrFriedParts
I will be answering point by point for my own opinion. 1) Yes, you're right! We can change it to be "cars moving in streets in general". Not necessarily highways. 2) Well, yes and no! Electron to electron collision is also one of the reasons of resistances. It's not all about the collision with the edges of the path. So if collisions in general were decreased no matter with what the electrons are colliding with, the theory still holds fine. 3) Yes, but when you have more collisions there are more energy loss in the form of heat. Note that you said "almost" completely elastic. - Adel Bibi
Adel Bibi
You still do not correctly grasp how this works. Your response to (2) fails to grasp the basic physics. The electrons don't physically collide (like charges repel), but they do interact through the static forces. This makes the electrons behave like waves (not particles). It is the interference of the lattice structure (the metal/road) with the electrons that causes resistance.
DrFriedParts
This resistance is caused mainly by two things. One is impurities in the metal, which cause irregularities in the periodicity of the lattice. The other is the disturbance or "vibration" of the lattice caused by heat. Since some heat is always present (except at absolute zero) there is always some resistance from this source which prevents the electrons from sailing through.
DrFriedParts
You answer to (3) remains similarly confused. The possibility of collision for any single electron remains the same (it is a function of material, environment, and applied voltage). The larger the cross-sectional area of the conductor, the more electrons per unit length are available to carry the current. In the context of your analogy, the highway is always full of cars. Adding more lanes also adds more cars so more cars pass through the road per unit time even though the speed hasn't changed.
DrFriedParts
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A teacher explained why by using a highway analogy. The more lanes you have, the faster the cars go through, where the number of lanes obviously represent the wire thickness and the cars represent electrons. Easy enough.

What teacher should have said is :

  • Assume that cars travel at a constant speed and with constant spacing on a highway lane.
  • The amount of vehicles going past a point will be proportional to the number of lanes.
  • Increasing the number of lanes does not increase the speed of the vehicles. (Not quite true because cars are driven by people!)
Transistor
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This is a great question! - The highway / car is an excellent analogy

In this analogy, you have to consider these factors.

Your design will have a requirement for voltage - in our model, voltage is the SPEED the cars need to travel.

The design will have a requirement for current - the is the NUMBER OF CARS needed to travel down the highway. (or volume)

The wire size / resistance is the NUMBER OF LANES.

Wattage, or power, is the combination of both voltage * current, or the number of cars travelling down the highway in a given time.

The highway has to be designed to meet the specifications for both speed and volume. If you have a very small current requirement, say, 1 car, you'll only ever need a one lane highway, because your can can travel as fast as possible, (high voltage). But if you have a high current requirement, 10,000 cars, you'll need a 100 lane highway. (depending on power requirements)

But take for example, the power grid - a transmission line for a city of 1 million people. That is very roughly 300,000 households, each using 1 kw of power. That means our line needs to deliver 3 Gigawatts of power! You could do this with 1 V @ 3 giga-amps, or 3 GV @ 1 amp, or something in between.

What voltage / current would be required to make the transmission line as small as possible?

philbrooksjazz
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