Relax - you already knew this. Conductor resistance is a function of conductor temperature and conductor temperature is a function of amperage which is a function of restance.... Interesting circular influences there. Fortunately, as temperature increases so does resistance. Otherwise we'd always be battling a current/thermal runaway scenario. So, Ohm's Law is "close enough" for constant temperatures within limits. But, if you think that I = E/R is really an immutable "Law", hook up a 12vdc battery to an incandescent 12v lamp. With a dual trace o-scope, capture the applied voltage on one channel and the lamp current on the other during the short period that the fillament is heating up. Ohm's Law implies a linear curve - but what you capture is quite different. Of course, to get a current input you can measure the voltage across a very low valued resistor in series with the lamp which would also heat up and affect the outcome. But, choosing a very low resistance value helps minimize the resistor's influence.
Yeah - OK - I'm just killing time and fighting off boredom.
AT ANY given instantaneous moment in the observation, Ohm's LAW is 100% true with your bulb example. You have to think in terms of time, and relevance.
The COLD measured resistance of the filament, and the HOT measured resistance are two different values, but the reading at each level STILL yields the EXACT equation results.
How can you not see that FACT?
If the wires feeding a circuit when cold are 0.1 ohm, and when warm are
0.2 ohms, the values of your simulation of that circuit need to show those parasitic element differences at those different times of operation and observation.
The laws still carry thorough when your values are corrected for EVERY moment in time that you are making your observations. AT NO TIME are they in error. If you have an error in your measurement, YOU are not including an element of the operation of the circuit you are observing.
You're claiming that I = E/R, but this suggests that if you first know E and first know R, that you can then ascertain I.
I defy you to do that: In other words, given a unknown circuit element, I want you to determine the resistance R without first measuring I. I don't think it can be done.
-------------------------------- Not really- actually you are wrong (and this is a common error). Doug's statements are closer to the truth. Ohms law (as Ohm determined from experimental measurements) is actually only valid in the linear case where E/I is constant independent of either E or I. He noted a linear relationship between E and I. In other words, R is constant so that if E doubles, I doubles. Hence, Ohm's Law, strictly speaking, is not valid for a lightbulb as any change in current (or applied voltage) changes the resistance. It is also not valid for a diode or transistor. Look at the definition of Ohm's Law. (See below) Note the terms "Linear", "proportional", constant of proportionality.
Ohm's Law is not V=IR EXCEPT when R is constant.
Yes, in a given situation, you can measure V and I and call the result R. If the voltage changes, I changes and unless the device is linear, R changes. In that situation, R is actually quite meaningless as a quantity because it gives no useful information that you don't already have and cannot be used to predict anything if V changes(there is an infinite set of V-I curves going through that point -which one is it?)- all you can say from a measurement at a point is that I =some unknown function of V for which you have one point. You can't predict , from data at that point, that a change in voltage will cause a given change in current.
Ohm's tests indicated that within limits, V=a+b*I (equation of a straight line) becomes V=R*I for many materials. We are lucky that that is so (or can be treated as such for small variations) because linearity is the basis of being able to use series and parallel equivalents, Thevenin, etc.
In fact Ohm's Law and our well beloved circuit theorems (except Kirchoff's Laws) are so much ratshit in non-linear circuits. We tend to forget that (or never learned it in the first place).
Here is an excerpt from
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"1. Ohm's Law deals with the relationship between voltage and current in an ideal conductor. This relationship states that: The potential difference (voltage) across an ideal conductor is proportional to the current through it.
The constant of proportionality is called the "resistance", R.
Ohm's Law is given by:
V = I R where V is the potential difference between two points which include a resistance R. I is the current flowing through the resistance. For biological work, it is often preferable to use the conductance, g = 1/R; In this form Ohm's Law is: I = g V
Material that obeys Ohm's Law is called "ohmic" or "linear" because the potential difference across it varies linearly with the current. "
The initial current, and ANY instantaneous current at ANY TIME during ANY instantaneous observation WILL follow the law to the letter!
That is the whole point. OF COURSE it varies as it heats up. That, however, does NOT negate the law. It is STILL a "pure resistance".
It matters not that it changes with temperature, only that the observer KNOWS that it does, and KNOWS that that is the reason for any given instantaneous reading to differ from any other during the period of observation. The law remains the same. Your knowledge of what takes place as a flowing current mutates the value of that resistive element is what you need to change. As it changes, the current does as well. That FURTHER proves the law, not disproves it.
The amount of current flowing in a circuit MADE UP OF PURE RESISTANCES is directly proportional to the electromotive forces impressed on the circuit, and inversely proportional to the total RESISTANCE of the circuit.
The term "linear" does not appear in what Ohm wrote, regardless of whether it is applicable.
At ANY given instance during the observation of the illumination period of the light bulb, all equations and readings taken STILL match the law, and there is nothing you can do about it. It doesn't matter that the resistance changes. ANY readings taken at any point in time during said change OR even after all settling has occurred, STILL follows the law.
Really! Which Maxwell equation would you use? J = sigma * E ?
Ohm's law, to the extent that it is a law is a property of solid state material, usually a metal. It assumes that carrier get accelerated by an electric field and then get scattered from impurities, phonons, or other lattice imperfections, and that there is a mean free path between collisions. How does that arise from Maxwell equations alone?
In a purely resistive circuit, fix one element E,I or R, vary a second element, the formula predicts the value of the third element. Seems pedantic and innaccurate to insist it applies only when R is fixed.
Great Attractor's viewpoint is a whole bunch more practical, and it is accurate.
And that is where you have hung yourself. I could apply a voltage to a diode and measure a current. Then according to what you have said, I could then say R=E/I and this would agree with what you have emphatically said. was Ohms Law. Now I have a PURELY RESISTIVE element where R is not independent of E or I - that is non-linear as is the case for a light bulb (purely resistive element) or a diode (again purely resistive ). Non-linear purely resistive elements exist. Again- where is Ohm's Law useful? Where Ohm said it was- in the case (and limited range) where E/I is constant independent of either E or I. If your lightbulb filament could be kept at a constant temperature, it would obey Ohm's Law as then the resistance would be constant. Otherwise, as you said R=E/I holds at any given operating point BUT it is not Ohm's Law nor is it useful information.
In other words, you have now recognised that there is a qualifier- without recognising that the qualifier is that the element is operating in the range where it is linear. That is R is constant- independent of E and I- and we are back to what I (and the reference that I gave you, said). That is the qualifier that is generally recognised.
Don Kelly snipped-for-privacy@shawcross.ca remove the X to answer
It is pedantic but happens to be important and is correct. What is the point of saying R=V/I from observed V and I at a single measurement? Does it give any useful or practical information as you already know V and I for that situation? Suppose that I have measured 1A when I applied 10V so R =10ohms- so if I apply 10V I know that I=1A (which I already know-ho-hum what else is new? That is what I measured).
If I apply 20V, I simply don't know that R is still 10 ohms and can't predict I.
Tell me the practicality of that? I can fix V and vary I and calculate an R but I have to know both V and I to do that -so??? No useful information is obtained. If, I did this for several points, I could discern a relationship between V and I (which are actually measured quantities -R isn't) and come up with some useful relationship such as V=2I or V=3I^5 or V=2/I etc. Ohm found that within limits, for common conductors of his day, V=(constant)*I which is a linear relationship. THAT is Ohm's Law. Be thankful that it does work very well in most situations.
How does one get a known relationship from one data point? Sure you can do that- for example you can fix R=10 ohms and then say "for V= 10, 20, 30 V , the current is 1, 2, 3 A" but is this meaningful if you don't actually know that R is constant? To do so means that you have assumed that resistance is constant as an act of faith. In the lightbulb, you have a purely resistive element and, if you could keep the filament temperature constant, then you could "fix" R and do some prediction. However, that situation doesn't occur so you have a purely resistive element which is non-ohmic -that is , it does't obey Ohm's Law. In this case, "fixing" the resistance gives a model which doesn't represent the real device.
You and Attractor seem to be confusing "Purely Resistive" with constant R (or V linearly proportional to I)- that is "ohmic". Tain't necessarily so. The usefulness of Ohm's Law is when it can be used in the sense that I have used it- If R is constant one can then determine what happens for different voltages across the element. Here's a little problem for you:
Measurements on an unknown purely resistive element give a current of 1A at
10V The voltage is raised to 20V, what is the current?
Problem 2
Element 1 I=0.001*V^3 (1A at 10V or 10 ohms at this point) Now you have useful information on the V-I relationship which is not given by saying the resistance is 10ohms at 10V) Element 2 R=5ohm constant Find I for the series combination. (it isn't 0.67A) You will have to do a bit of work here- but consider if the circuit was more complex.
In fact, "The Great Attractor" is absolutely wrong. I know that V=I*R is too often incorrectly called Ohm's Law but the only reason that it is of any importance is that resistance materials often have a linear V-I relationship (within limits). His "education" seems to have missed that. The reference I gave indicates that.
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several references- all of which emphasise direct proportionality -i.e linearity.
"The Great Attractor" (could he be a re-incarnation of Fats (Bytesass ??) simply hasn't done his homework. Even Wikipedia has done much better (but has a non-sensical statement as Ohm's Law doesn't depend on the definition of the ohm.)
The only issue I see is the pedantry causes confusion. Are you saying, beyond that, that the formula V = IR does not yield accurate results when you know two of the values and solve for the third?
Real world, change any one of the values and you may change both of the other values. The voltage may sag or rise when you change the resistance, or the current that the supply could provide at
10V might not be available at 20 V. The resistance changes with delta T and T changes with delta I and I changes with delta V and delta R, by the formula V = IR.
V = IR is useful for fixed or variable resistances. It's used all the time for both pots and fixed resistances.
Answering the question you ask below: say you have a load that works exactly how you want it to when it is in series with a 60 watt light bulb. You measure V and I, determine R of the bulb, and install a resistor of that value. Useful and practical information.
The law specifically states that it ONLY applies to such circuits, and yes, all elements are to be considered. The wires, the contacts, the "resistor" load itself... all are PART of the circuit, and is all are "purely resistive" or as you state "ohmic", then they get included.
Very few physical laws are truly inviolable. These range from Newton's laws that are only an approximation to Einstein's various relativity theories to superposition in electrical phenomena such as Maxwell's equations. Think frequency multiplication of light.
The utility of physical law is that it applies well enough over a range of conditions so that it can be used for reliable calculations. Ohm's law is that kind of a law.
You can buy resistors labeled by their resistance from which you can design and construct circuits such as transistor amplifiers in which the transistors themselves do not follow Ohm's law. Ohm's law is good enough for that.
But do not put 3,000V across a 10M? 1W resistor (below the calculated power dissipation). You would soon find out that there are problems with Ohm's law.
-------------- It appears that we agree. My "not really" implies that if one or more elements are not "ohmic" then Ohm's law cannot be extended to the whole circuit. I should have been clearer.
Any circuit theorem (except Kirchoff's laws) or combination of components (eg. series,parallel) depends on linearity -R constant (or ohmic) in V=IR for all resistive elements. It is linearity which makes these tools possible (and is the basis of Ohm's law).
I avoid "purely resistive" as there are purely resistivive elements for which Ohms law doesn't apply. For example carbon brushes used in DC machines often exhibit a nearly constant voltage drop over a range of currents. Other non-linear resistors exist and do not obey Ohm's Law.
One does not EVER put the rated power through a resistor. They are ALL meant to be utilzed in designs that only tax them at one half to two thirds of their rating. Any good designer would not only know this basic tenet, but would design any resistor location to follow it. The main reason is that any resistor that one does dissipate the rated power in will be so hot, any nearby component, or PCB surfaces WILL get damaged by the heat it exhibits.
If you use a resistor rated for HV, then any voltage you put across it below that should be below the power rating, and should not stress the resistor so greatly that the resistance value moves appreciably.
I have used SEVERAL sizes of 10MOhm through 10GOhm HV resistors, and they don't move much under stress, and any movement they do express can be compensated for with feed forward capacitance, or other methods, but that is all on a circuit by circuit basis.
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