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Please read this:

Source.

How does the resistance of a wire depend on its length?

... The analogy used is that of a crowded place.

If you want to move through a crowd, if there is more space, then it’s easier (hence inversely related to A), and if the crowd is ‘longer’ it takes more time to make it across.

The first part makes sense, more space, means easier to move through, but I always had this problem with the second part of the analogy. It just didn’t make sense.

Let me be more specific.

Current is proportional to the speed of the charged particles. So in the crowd analogy, the current is proportional to the speed at which you can make it through. What does your speed have anything to do with the length of the crowd? ... If you think of it this way, the resistance shouldn’t depend on the length at all. How could the material start resisting more at one place, just by adding another wire at some other place? ...

The key is to understand that charges are being pushed through the wire due to an electric field. When the wire is short, the electric field is more concentrated and hence stronger. If the wire is doubled in length, the electric field gets more diluted and reduces to half its strength.

This is why increasing the length of wire, reduces the speed of the charges and hence translates to increasing the resistance of the wire. ... Let’s get back to that crowd and imagine you and your friends are trying to make it through the crowd. The important thing is there is someone externally providing energy to you and your friends to move through the crowd. Now only those of you need energy who are within the crowd length. Your friends outside the crowd length don’t need any energy as there is no opposition.

Now if the crowd length doubles, then twice the number of people are trying to make it through the crowd. But the external total energy remains the same. And so when distributed, each of you gets half as much as you got before, and hence you end up moving slower. ... And this why resistance increases with length because for a given voltage, lesser energy is transferred to each electron.

I found this answer to be most satisfying for answering of why current decrease when length increase, but if we extend this analogy or explanation towards area, than in area increase there should be atom increase, i.e electron increase, that should lead to high resistance according to above link answer.

Many say that when the area increases, the space to move increases. That gives a low resistance. Don't you think area increase means electron increase so how could there be more space? Really no logic? They are seeing it as amount of electrons remain the same just the area increases. That is not possible. The more metal, the more free electrons?

Could anyone tell me where I am wrong or give a satisfying explanation for both area, length concept all together?

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  • \$\begingroup\$ More area means more charges can cross a given cross-section of the conductor in given time; means more current, means less resistance. \$\endgroup\$
    – Mitu Raj
    Aug 17, 2021 at 5:18
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    \$\begingroup\$ @anshika can you take quotes from the article and cite them with a source, The link might go down and it would make a better question if you could do that thanks \$\endgroup\$
    – Voltage Spike
    Aug 17, 2021 at 6:01
  • \$\begingroup\$ @volatage spike,sir it actually a explanation of a paragraph so its hard to oaste as it is too long and can make question and reading worse.😔 \$\endgroup\$ Aug 17, 2021 at 6:20
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    \$\begingroup\$ When the area increases, the electric field doesn't get "diluted". Electric field would be potential difference / length; area doesn't come into picture. When length increases the electric filed for the same potential difference would be smaller ("diluted"). So, even if you increase the area, the electric field remains the same. \$\endgroup\$
    – AJN
    Aug 17, 2021 at 12:33
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    \$\begingroup\$ "So in the crowd analogy, the current is proportional to the speed at which you can make it through." That's not correct. If the corridor is full you just push a person in at the back and one immediately falls out at the front. \$\endgroup\$
    – Transistor
    Aug 17, 2021 at 12:58

4 Answers 4

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This might be a case where the water analogy is useful.

Imagine a pipe. Voltage is analogous to pressure, so let's say that is fixed. The volume of water that flows is analogous to the current, so the ratio of pressure over volume is analogous to resistance.

The larger the cross-sectional area of the pipe, the more water flows (like a resistance decrease).

The longer the pipe, for a given cross-sectional area, the less water flows (like a resistance increase).

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  • \$\begingroup\$ Sir please read that link. I have heard these answers many time. But when u will read that link u will get what i m trying to ask. Thank u🙏 \$\endgroup\$ Aug 17, 2021 at 6:22
  • \$\begingroup\$ @Anshikasingh You need to explain what you are trying to ask - pointing to another question and expecting an answer to that question just confuses the system. That question has answers and your question - good or bad at representing your “real” issue, has answers. \$\endgroup\$
    – Solar Mike
    Aug 17, 2021 at 7:44
  • \$\begingroup\$ sir i am trying to ask that according to given link hus explanation for L being proportional to R is satisfying. But if i extend his reasoning on cross section area factor...... It is confusing me. Because according to him e- increase means electric field diluted(hope u read the Link) therefore decreasing current means R increase, but see if we see Area case in that, if area increase obviously there are atoms increase, make sense! Atom increase= free e- increase. Than it should too lead to dilution of electric field according to that link explanation.... \$\endgroup\$ Aug 17, 2021 at 9:50
  • \$\begingroup\$ And this should too lead to low current and means high resistance..as in Length case he explains.hope u r getting what i am saying sir😔 \$\endgroup\$ Aug 17, 2021 at 9:50
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    \$\begingroup\$ No need to address anyone as 'sir' here. By the way, you think in complex manner. If area increases, amount of charge flow increases, isn't that enough to explain the decrease in resistance? If there are 1000 people in a room, a small door or a big door will ease the movement of people to come out of it? @Anshikasingh \$\endgroup\$
    – Mitu Raj
    Aug 17, 2021 at 10:36
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Think of the resistance as something like the number of collisions between the charge carriers and the atoms of the compound/material of the resistor: The longer the material, the more collisions, hence the higher resistance you get. The resistivity (\$\rho\$) which has a unit of \$\mathrm{\Omega\cdot m}\$ may give you a clue about this.

If you increase the cross-sectional area of the resistor, you just decrease the possible number of collisions: The lesser the collisions, the lower resistance you get.

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    \$\begingroup\$ "If you increase the cross-sectional area of the resistor, you just decrease the possible number of collisions" - Why? \$\endgroup\$ Aug 17, 2021 at 5:15
  • \$\begingroup\$ @BruceAbbott water analogy: for the same amount of water flow, if you increase the area of the pipe, the number of possible collisions between the pipe's total inner surface and the water molecules will decrease. \$\endgroup\$ Aug 17, 2021 at 5:30
  • \$\begingroup\$ Dont u think increase area also increase no. Of electrons? Thus collision arent affectively reduce!!??? 🤔🤔🤔🤔 \$\endgroup\$ Aug 17, 2021 at 6:19
  • \$\begingroup\$ @Anshikasingh increasing the area increases the number of electrons, yes. But, if you keep the current (i.e. the number of carriers) the same, these carriers will spread across the area (assuming DC) and the total (and averagre) num of collisions will decrease. \$\endgroup\$ Aug 17, 2021 at 18:42
  • \$\begingroup\$ @Rohat kilic, can u please explain ☹️ how current or carrer would be same? Please elaborate ur point sir🙏 \$\endgroup\$ Aug 18, 2021 at 3:19
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Answering because the comments got long.

If the wire is doubled in length, the electric field gets more diluted and reduces to half its strength ...

Could u explain more what actually "dilution" of electric field u meant?

What the originator of the analogy probably means by dilution is the reduction in electric field when length increases since E = V / L. This of course assumes that V is fixed.

Assuming V is fixed, when the area increases, the electric field doesn't get "diluted". Electric field would be potential difference / length; area doesn't come into picture. When length increases the electric field for the same potential difference would be smaller ("diluted"). So, even if you increase the area, the electric field remains the same*.

Doesn't electric field depend on electron amount increase as happen in BOTH Length as well as AREA?

The circuit that we must imagine (I assume) while reading this analogy, is a cell or battery connected to a resistive material. The battery fixes the potential difference between the resistor terminals (e.g. 1.5 V AA cell).

The length of the resistor then fixes the electric field inside the resistor (potential difference imposed by the battery divided by length of the resistor).

The area doesn't affect either the V or the E*.

The number of free electrons also doesn't affect V or E*.

Doesn't electric field depend on electron amount ...

No*.

  1. If you are talking about free electrons in the resistive material that contribute to it being a (bad) conductor, then remember that their charge and electric field are neutralized by the positive charge of nucleus of the atoms from which they come from.
  2. If you are talking about excess electrons (e.g. that we learn in electrostatics), remember that such isolated / excess electrons are not present in most circuits*.
  3. So the cell / battery is the only source of electric field / potential difference*.

* There are likely a lot of assumptions left unsaid.

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  • \$\begingroup\$ Ooo!!! FINALLY! Thanks a million and billion times sir🙏. And yah u ask me n... What i meant by dilution of electric field is ..... I thought ' as no. Of e- increase the force (accelaration ) on each electron get decrease ' thats why i thought as no of e- increase in area too than why electric field not diluted? 😅 may be thats why i got wrong? Isnt it? BTW what u really meant by dilution of electric field???? May be there i m getting wrong🤔 \$\endgroup\$ Aug 18, 2021 at 3:25
  • \$\begingroup\$ Now can You explain clearly why resustance decrease when area increase? Please? \$\endgroup\$ Aug 18, 2021 at 4:24
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Resistance depends on an object’s size, shape, and material. Electric current flows when electrons move through a conductor, such as a metal wire. The moving electrons can collide with the ions in the metal. This makes it more difficult for the current to flow, and causes resistance.

The resistance of a long wire is greater than the resistance of a short wire because electrons collide with more ions as they pass through. The relationship between resistance and wire length is directly proportional.

The resistance of a thin wire is greater than the resistance of a thick wire because a thin wire has fewer electrons to carry the current. The relationship between resistance and the area of the cross section of a wire is inversely proportional.

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  • \$\begingroup\$ Sir please read that link. I have heard these answers many time. But when u will read that link u will get what i m trying to ask. Thank u🙏 \$\endgroup\$ Aug 17, 2021 at 6:23
  • \$\begingroup\$ @Anshikasingh you should explain what you are trying to ask. \$\endgroup\$
    – Solar Mike
    Aug 17, 2021 at 7:41
  • \$\begingroup\$ @solar mike, sir i am trying to ask that according to given link hus explanation for L being proportional to R is satisfying. But if i extend his reasoning on cross section area factor...... It is confusing me. Because according to him e- increase means electric field diluted(hope u read the Link) therefore decreasing current means R increase, but see if we see Area case in that, if area increase obviously there are atoms increase, make sense! Atom increase= free e- increase. Than it should too lead to dilution of electric field according to that link explanation.... \$\endgroup\$ Aug 17, 2021 at 9:48
  • \$\begingroup\$ And this should too lead to low current and means high resistance..as in Length case he explains.hope u r getting what i am saying sir😔 \$\endgroup\$ Aug 17, 2021 at 9:49

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