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Are there some other ways to deduce resistance from current, than Ohm's Law (e.g. because why'd we assume a linear relationship?)?

Also, are Kirchoff's laws usually often in conjunction with Ohm's Law, because aren't

$$\sum I=0, \sum V=0$$

slightly useless for practical purposes on their own (without adding Ohm's Law to the above)?

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    $\begingroup$ I kind of think of Ohm's Law as being the definition of resistance. I'm not sure what you'd use as your definition of resistance, if you were hoping to somehow calculate it without using Ohm's Law. $\endgroup$
    – Dawood ibn Kareem
    Commented Feb 4, 2018 at 9:28
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    $\begingroup$ One could measure ohmic heating by calorimetry, using $P = I^2R$. $\endgroup$
    – user137289
    Commented Feb 4, 2018 at 9:41
  • $\begingroup$ How is Ohm's law or Kirchhoff's laws "slightly useless for practical purposes"? It is the most used laws in the first steps of electronics design. $\endgroup$
    – Steeven
    Commented Feb 4, 2018 at 9:43
  • $\begingroup$ Resistance is the inverse of conductivity. $\endgroup$
    – user34793
    Commented Feb 4, 2018 at 9:56
  • $\begingroup$ @Steeven I wrote that only Kirchoff's laws (without Ohm's Law) seem to be useless on their own. For practical purposes. $\endgroup$
    – mavavilj
    Commented Feb 4, 2018 at 10:17

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Kirchhoff's laws (two h's in Kirchhoff) are relationships that hold, in the quasi-static limit, between voltages and currents in a circuit, regardless of the nature of the elements in the circuit. Whether you have a circuit composed of resistors, capacitors and transistors, and one composed of potatoes, carrots and bananas, Kirchhoff's laws hold.

Ohm's law is a so-called constitutive equation, that is, a relation that specifies the behaviour of a certain circuit element; in this case, the two-terminal linear resistor. From the point of view of circuit theory, Ohm's law actually defines the linear resistor: it is that element for which the voltage across its terminals is directly proportional to the current crossing the element, and the coefficient of proportionality is called resistance.

Therefore, you "deduce" or, rather, you directly calculate, determine or measure the resistance by employing its very definition, as you would do for any other quantity.

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  • $\begingroup$ So Ohm's Law equates to the definition of resistance? $\endgroup$
    – mavavilj
    Commented Feb 4, 2018 at 10:19
  • $\begingroup$ @mavavilj Yes, Ohm's law gives the definition of resistance. $\endgroup$
    – Massimo Ortolano
    Commented Feb 4, 2018 at 10:20
  • $\begingroup$ The Wikipedia page for resistance is pretty oddly worded. en.wikipedia.org/wiki/Electrical_resistance_and_conductance. It writes that the definition of resistance is $R=V/I$. Then writes that "this proportionality is called Ohm's Law" . As if the proportionality and the definition would be different things. $\endgroup$
    – mavavilj
    Commented Feb 4, 2018 at 10:55
  • $\begingroup$ @MassimoOrtolano You do not need Ohm’s law to define resistance. $\endgroup$
    – Farcher
    Commented Feb 4, 2018 at 11:55
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    $\begingroup$ @Farcher You can certainly define the resistance as the ratio of the voltage across any two-terminal resistor, linear – obeying Ohm's law – or not, and the current through it. However, for nonlinear resistors, such a definition is usually not particularly useful and can be also misleading; and you can also define a differential resistance or, for nonlinear circuits with reactive elements, a resistance defined in terms of dissipated power. This is why I restricted the above definition to linear resistors, as is done by most authors. $\endgroup$
    – Massimo Ortolano
    Commented Feb 4, 2018 at 12:15

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