Mengapa ketebalan kawat mempengaruhi resistansi?

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?

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.

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 )}

$\frac{1}{R_{Total}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} ... \frac{1}{R_n}$

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 = \frac{1}{R}$$G$$R$

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

$Conductance = G_{Total} = G_1 + G_2 + G_3 .. G_n = \frac{1}{R_{Total}}= \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} ... \frac{1}{R_n}$

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).

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.

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.

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.

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!)

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?