Resistivity = (Resistance times area ) divided by length  $$\rho = (RA)/l$$  now my question is that in order to calculate the resistivity for some metal we have to take into account its length and area then why is it said that the resistivity of a metal is independent of its area or length . i.e. Why does every piece of copper have the same resistivity regardless of its area or length?
121910
The formula for resistivity is: $$\rho = \frac{RA}{L}$$  where $\rho$ is resistivity,  $R$ is resistance, $A$ is cross-sectional area, and $L$ is the length of the conductor.    We can see from the formula that $A$ and $L$ are involved, why then does resistivity not depend on dimensions?
25748
Ohm is defined as      "a resistance between two points of a conductor when a constant potential difference of 1.0 volt, applied to these points, produces in the conductor a current of 1.0 ampere, the conductor not being the seat of any electromotive force"    according to  wikipedia page. However, I still don't understand what exactly is resistance and ohm. Does resistance decrease the amount of electrons passing through a conductor per unit time or does it decrease the energy that a single electron carries or none of them? I know what Ohm law is and I also know the mathematical background of resistance but I can not understand the logic behind it.   For example, when we talk about a conductor that should be insulated by an electrical insulator we have to know how many ohms that is needed to determine the size of the insulator for a good insulation. But I would like to know how it is determined. Thus, I would be pleased if someone could explain the logical background of resistance and ohm. Thanks.
48045
When we have resistors in series, the current through all the resistors is same and the voltage drop (or simply voltage) at each resistor is different.  Question 1: It is fine that voltage drop (potential drop) across each resistor is different because each resistor offers different resistance (suppose). but how is the current through each resistor same? If we have resistors of different resistance, shouldn't the current be different through each resistor?  Similarly, when we have resistors in parallel, the current through each resistor is different but the voltage drop at each resistor is same.  Question 2: Current through each resistor is different because resistance of each resistor is different (suppose). but how is the voltage drop across each resistor same here? Shouldn't the voltage drop at each resistor be different because each resistor offers different resistance?
43576
It took me a long time to understand that current is constant throughout the circuit. And now I am stuck at one last thing: The speed of charge. Here is what I am thinking:  Current is defined as quantity of charge passing through a point at a given time, and from this we can deduce that current is constant throughout a circuit. But, if this is true, then wouldn't the speed of charge through a resistor be increased? Let us think about an analogy, water flowing through a pipe. Suppose water is flowing through a broader pipe(analogous to a less-resistance wire), and  a greater quantity of water can flow past a point because of larger cross-sectional area. Now, suddenly water encounters a smaller pipe(analogous to the resistor). So, less quantity of charge can flow through it because of less cross-sectional area. But, if the volume of water flowing in a time $T$(analogous to current) is same, won't the rate of flow of water in the narrower pipe(the resistor) be more?  I am asking this question because while seeing some answers for the question that "Why is current constant?" , I saw some people saying that speed of charge slows down a bit through a resistor, which seems incorrect to me.
120006
So, for my science fair I had to test the gauge of a copper wire vs electrical resistance. What I did was I set up a series circuit involving a 6v battery, a light bulb, a multimeter, and a voltmeter. I would change out three different wires with three different gauges.   For the 4-gauge wire, I got 0.004V and 0.04A. For the 8-gauge wire, I got 0.003V and 0.04A For the 12-gauge wire, I got 0.001V and 0.04A.   In this experiment, what would the independent and dependent variables?  We also have to fill out a table like this:
41980
If you have a circuit of a battery, a Resistance and a light connected with a wire by example: in the middle the wire is cutted in two pieces. if you connect each piece of wire with a metal object and put those twee metal objects together so the current can flow to the resistance and the light. How is it possible that the electrons can flow from the wire to one of the metal objects into the other metal object and again in the wire? I do understand how electrons move in metals and wires, but i don't know how the transaction of electrons between those components goes. Is it really that simple that electrons just can flow from one object into another of is the (kinetic) energy passed through when an electron clashes with the edge and that energie is passed through to the other object?
84193
Let's imagine that we have a tridimensional metal object of infinite size, and decide to calculate the resistance between two arbitrary points. How would we go about doing this?  I have thought of two possibilities for calculating this, the first one being an adaptation of the conductivity (S/m) using the Pythagorean theorem to find a distance and isolating the resistance from there, treating it like we would treat an electrolytic liquid.  The second possibility I have been thinking about would be a 3-dimentional adaptation of the infinite-resistors problem (which I have only seen in 2d).  Would one of these methods result in giving a decent approximation, or would another method give better results?
56587
I know the reasons for using terminating resistors on a  and how important it is.  But why 120&nbsp;ohm? How did this value come up? Is there any specific reason to use 120&nbsp;ohm?
90504
If we look at $P=VI$, we see that if the current doubles then the potential difference is halved but this doesn't seem to make sense according to $V=IR$. If we look at that equation, since the resistance remains constant, doubling the current should increase the potential difference. Can someone explain what I'm misunderstanding in simple terminology?
86457
I know the friction is given by the following equation $$\mu F_N=F_f$$  which tells me friction is independent of surface area, but how do I characterize it as such if I want to add surface area into my equation what would the equation be?  We all know friction is a function of the normal reaction exerted on the body and the coefficient of friction. How is this coefficient derived, any equation? Or is it all experimental? Any quantum mechanical explanation for friction?
33285
Why does resistivity increase with temperature?  The explanations I have heard so far are that increasing temperature increases vibrations in the lattice structure resulting in the number of collisions increasing.  But the vibrations from thermal energy are random, so around half of the vibrations would result in the atoms moving out of the electrons way and half would result in atoms moving into the way of the electrons.  And since half of the vibrations result in increasing the drift speed and half reduce it, shouldn't the average drift speed remain the same?
26320
Shouldn't the current passing through a resistor be lesser than that which passes through a circuit? My understanding is that since Current = Charges/Time. If there exists a resistance to the flow of charges, then that must mean the charges slow down, meaning that more time is required to pass through a point. So, the current should then decrease. But, since this opposition to the flow of charges doesn't exist in the ENTIRE circuit, it should really only decrease the current in the resistor, right? Am I confusing the resistance of the resistor with the resistance of the wire? Any help will be appreciated! Thanks a bunch for lending me some of your time :D
71085
In an ideal circuit, How can there be a current b/w points a &amp; b, when there is no potential difference and thus no electric field between a &amp; b? If there is no current, then where does current across the resistor come from, because that means no charge is coming from the battery (?).
17703
OK, very basic question here.  I read lots of books, searched quite a bit, and every description I read seemed to talk about the flow of electrons and right away go too deep in theory for me to grasp the basic principle of their use.  I understand a resistor limits the "flow", so that an LED doesn't blow up for example. But I fail to understand exactly what a resistor does to current and voltage...  Do resistors affect both current and voltage? In what manner?
962
I am confused whether drift velocity depends upon area or not . I checked answers for this question but all of them were cancelling each other out . from the equation $$I = neAv$$ It is clear that drift velocity should depend upon area but at the same time don't you think that by increasing the area of cross section of a conductor should have resulted in increase in drift velocity please help me out with it in detailed answer of how should i go with all the possible cases and explanation ,thanks :)
110568
I cannot understand how 3-wire measurement will improve the resistance measurement.    They say that IF lead resistance \$ R_L \$ is the same, it will compensate. How can this happen?  If bridge is balanced (without \$ R_L \$):  \$ \frac {R_1}{R_2} = \frac {R_g}{R_3} \$  If \$ R_L \$ is added: \$ \frac {R1}{R2}= \frac {R_g+R_L}{R_3+R_L} \$  \$ \frac {R_g}{R_3} \$ is not same as \$ \frac {R_g+R_L}{R_3+R_L}\$; is this true only if \$ R_G=R_3 \$ in the beginning? So this means that \$R_L\$ does not get compensated?
68328
This is based on a problem that came up today. During the course of this problem I realized that I wasn't so sure I understood the relationship between wattage and heat produced.   In the past we did a test in the lab using .305 Ω /ft wire. The jacket is rated for 150C. We were able to get about 6.5A (at 3.66V)  out of it at 24C ambient, with out exceeding the jacket rating. I want to estimate what the ampacity of 0.027  Ω/ft wire is. So I am wondering if I did it correctly, because this amperage seems a little high for the wire to handle, then again most copper wire is only rated at 90C.  So the math I did on it was this  So you do .305 * 2 = .61 Ω /ft 6A^2 * .61 Ω = 21.62W   (I^2*r = W) 21.96W * / 2ft = 10.98 W/ ft  So would it be safe to assume that if I did the same with a 0.027w/ft wire with the same jacked I would arrive at this amperage?  If you start with 11W/ft * 2ft = 22W  0.027 Ω * 2ft = .054 Ω Sqrt(22W/(0.054 Ω)) = 20.18A  ETA: we are planning on testing this tomorrow when we get some wire in. So we shall find out.