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36

In addition to the other answers, here is something for the intuition: $$V=RI$$ More "pressure" $V$ is required to keep the flow $I$ of charges constant when the flow is resisted by $R$. They are resisted because the carges collide with a lot of particles along the way (or because the material is too narrow (a thin wire has higher resistance than a thick ...


25

Nerd Sniping! The answer is $\frac{4}{\pi} - \frac{1}{2}$. Simple explanation: http://www.mbeckler.org/resistor_grid/ Mathematical derivation: http://www.mathpages.com/home/kmath668/kmath668.htm


20

The identity $$ V = K \frac{dV}{dt} $$ is only guaranteed with a constant $K$ if your assumptions actually hold. The first identity $V=RI$ only holds for a resistor, while the other holds for a capacitor. So in this sense, the letters $V,I$ in these equations mean something else. In one of them, it's the current through (or voltage on) a particular resistor, ...


16

The physical 'meaning' of the imaginary part of the impedance is that it represents the energy storage part of the circuit element. To see this, let the sinusoidal current $i = I\cos(\omega t)$ be the current through a series RL circuit. The voltage across the combination is $$v = Ri + L\frac{di}{dt} = RI\cos(\omega t) - \omega LI\sin(\omega t)$$ The ...


16

It's not true. To see this, you can try an experiment with some batteries and light bulbs. Hook up two bulbs of different wattages (that is, with different resistances) in parallel with a single battery: ------------------------------------------ | | | Battery Bulb 1 Bulb 2 | ...


16

It depends on the internal resistance of the source. Fist consider a "voltage supply". What does "voltage supply" even mean? A voltage supply is supposed to output a fixed voltage no matter what we connect it to. Is this even possible? Suppose we connect the two terminals of the voltage supply together through a piece of wire, i.e. a really low resistance ...


15

Start with the initial diagram, but let's color code everything: Now move some wires around, without actually changing the connectivity: Finally, rotate the left and right blocks while again not changing the connectivity:


15

Perhaps I can clarify what I'm trying to get at with the famous waterwheel analogy 99 years ago, Nehemiah Hawkins published what I think is a marginally better analogy: Fig. 38. — Hydrostatic analogy of fall of potential in an electrical circuit. Explanation of above diagram In this diagram, a pump at bottom centre is pumping water from right to ...


12

There is actually a student-friendly microscopic model how to derive the real Ohm's law $$\vec{j} = \sigma \vec{E}.$$ After its derivation you can transform it into the more common form using the answer by Nesp. The idea goes as following: We must start with the definition of current: $$I = \frac{\Delta Q}{\Delta t}.$$ So where does current come from? ...


12

Yes, it is possible. For example Kevin Brown did here and here including this table. so for the xkcd problem the answer is $-\frac{1}{2}+\frac{4}{\pi} \approx 0.773$.


11

An ideal resistor is defined as the two-terminal circuit element where the voltage across is proportional to the current through: $V_R = R \cdot I_R$ and the constant of proportionality, $R$, is, well, constant. A physical resistor has at least series inductance and parallel capacitance and can be modelled with ideal circuit elements as follows (for ...


11

Alfred got in before me, but I have a diagram! I've marked all continuous bits of wire in the same colour, and marked the corresponding colours on the ends of the resistors. A quick redraw later and I get: which is a lot simpler!


10

instead of thinking your body is empty and that a charged wire has to push electrons one by one through you and into the ground (blood is actually full of charge carriers), a better analogy would be a very long queue of pushy people. if the entrance to the apple store doesn't open, it doesn't matter how hard the guy at the back pushes--nothing moves. ...


10

Hmm your experiment sounds like a good idea but I think it'll be much harder than you're imagining. The resistance of wires is very low. After all, they are designed to conduct! Check out this table. 30 gage wire has a resistance of $0.1\: \Omega/\mathrm{ft}$ which is well below what a typical multimeter can read. Also, because the resistance is so low, ...


9

Think of plumbing for a close analogy. Voltage is how hard you are pushing, and current is how much flows. The relationship writes itself: why would you get more or less flow from the same pump? The measure of how much effort is used to get flow (it makes more sense as the reciprical: how much flows for a unit of effort) is the interesting property, and ...


8

This isn't really an answer, because your question doesn't provide enough information for an answer. However it explains what you need to do. In fact this is exactly what I did (back in 1983!) to measure the resistivity of evaporated silver films. If you have the film formed on some substrate you need to score two lines to leave a long narrow track like ...


8

As others have noted, the big issue is getting the resistance of the wire into the range where your multimeter can measure it accurately. For that, the simple approach is to make the wires as long and thin as you can in order to maximize resistance. That said, another thing you can do is improve the precision of your measurements, e.g. by using ...


8

HINT: Notice that $$R_{eq}=R+\frac1{\frac1R+\frac1{R_{eq}}}$$


8

I find this sort of thing becomes much more intuitive if you can think of an analogy in terms of water. In this case, we can think of it like this: Here we have water flowing through a hole in a bath tub, into another tub underneath. The stick figure has been given the task of keeping the water level constant, by lifting water back up into the top tub ...


8

At sufficiently high voltages almost everything conducts due in part to quantum tunneling of electrons. An insulator has a breakdown voltage which is the field strength required before it will start conducting. Related to the breakdown voltage is the dielectric strength which is the minimum voltage over distance ($\mathrm{V}/\mathrm{m}$) before a material ...


8

Thermistor with this particular temperature behavior are commonly semiconductors. In a semi-conductor, there is an energy gap between the (filled) valence and the (empty) conduction band. At zero temperature, no charges are in the conduction band and the resistance should be infinite as the system behaves basically like an insulator. If you turn on the ...


7

I'll take it step by step here. First I'll write the answer for the first few cases with circuit analysis. Then I'll apply a reduction to show the pattern that the problem arrives at. N=1 $$Z = R+R=2R$$ N=2 $$Z = R+\frac{1}{\frac{1}{R}+\frac{1}{R + R}} = R \left( 1+\frac{1}{1+\frac{1}{1 + 1}} \right)=\frac{5}{3} R$$ N=3 $$Z = ...


7

I'll give the answer to this question using an unusual method that showed up in the American Mathematical Monthly's problem section perhaps in the late 1970s. This is not necessarily the easy way to solve the problem, but it works out nicely from an algebraic point of view. The way most people solve most resistance problems is to use series and parallel ...


7

Gregsan's and Kieran's answers are insightful analogies and the pushy electrons are certainly part of the answer. There is another aspect to the "decision" process and that is the propagation of electromagnetic waves. There is a chapter in the second volume of the Feynman Lectures on Physics - I don't have it with me but the relevant section will be just ...


7

Wire typically has very low resistance, so what you'll most likely end up measuring is the contact resistance.I.e., the resistance between your multimeter probes and the wire itself might have more resistance than your wire and overshadow it. My suggestion for the temperature dependent part would be to measure the resistance of the wire with it in boiling ...


7

This is true but strictly limited to RC circuits without external sources: that is, a resistor hooked up to a capacitor with nothing else in between. In that case, $V$ is indeed proportional to $\dot V$, with a crucial minus sign in between: $$ \dot V=-\frac1\tau V, $$ where $\tau>0$ is some constant. This equation implies that $V(t)=V(0)e^{-t/\tau}$, ...


7

Another possibility is that you are having to break through the oxide film that all Aluminium has in air. The voltage needed to do that can vary considerably. You might need to use sharp steel electrodes that will punch through the oxide and contact the metal directly.


7

Your original text admitted three interpretations, and I'm leaving the answers here: 1: What happens with a toy model when there's a circuit with an ideal battery and no resistance? All the charge moves around the circuit at one moment in time (infinite current). The energy must leave the system as Electromagnetic radiation - accelerating charges radiate, ...


7

Have you looked at Drude's model? I was taught something like that back at school and have kept it in mind as a intuitive way of understanding it. We want to understand why the current (rate of flow of charge) should be linear with the potential difference. The Drude idea is, as you noted, related to friction. Firstly, the EM field is linear in the ...


6

Think about current flow. If we take each individual resistor and determine the current for the applied voltage, we get: $$I_T=\frac {V}{R_1} +\frac {V}{R_2} + ...$$ Dividing everything by the voltage give us: $$\frac {I_T}{V}=\frac {1}{R_1} +\frac {1}{R_2} + ...$$ Which is the same as: $$\frac {1}{R_{eq}}=\frac {1}{R_1} +\frac {1}{R_2} + ...$$ Since there ...



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