Editing Ohm's law (section)

===Linear approximations===
{{See also|Small-signal modeling|Network analysis (electrical circuits)#Small signal equivalent circuit}}

Ohm's law is one of the basic equations used in the [[Network analysis (electrical circuits)|analysis of electrical circuits]]. It applies to both metal conductors and circuit components ([[resistor]]s) specifically made for this behaviour. Both are ubiquitous in electrical engineering. Materials and components that obey Ohm's law are described as "ohmic"<ref>Hughes, E, ''Electrical Technology'', pp10, Longmans, 1969.</ref> which means they produce the same value for resistance (''R'' = ''V''/''I'') regardless of the value of ''V'' or ''I'' which is applied and whether the applied voltage or current is DC ([[direct current]]) of either positive or negative polarity or AC ([[alternating current]]).

In a true ohmic device, the same value of resistance will be calculated from ''R'' = ''V''/''I'' regardless of the value of the applied voltage ''V''. That is, the ratio of ''V''/''I'' is constant, and when current is plotted as a function of voltage the curve is ''linear'' (a straight line). If voltage is forced to some value ''V'', then that voltage ''V'' divided by measured current ''I'' will equal ''R''. Or if the current is forced to some value ''I'', then the measured voltage ''V'' divided by that current ''I'' is also ''R''. Since the plot of ''I'' versus ''V'' is a straight line, then it is also true that for any set of two different voltages ''V''<sub>1</sub> and ''V''<sub>2</sub> applied across a given device of resistance ''R'', producing currents ''I''<sub>1</sub> = ''V''<sub>1</sub>/''R'' and ''I''<sub>2</sub> = ''V''<sub>2</sub>/''R'', that the ratio (''V''<sub>1</sub> − ''V''<sub>2</sub>)/(''I''<sub>1</sub> − ''I''<sub>2</sub>) is also a constant equal to ''R''. The operator "delta" (Δ) is used to represent a difference in a quantity, so we can write Δ''V'' = ''V''<sub>1</sub> − ''V''<sub>2</sub> and Δ''I'' = ''I''<sub>1</sub> − ''I''<sub>2</sub>. Summarizing, for any truly ohmic device having resistance ''R'', ''V''/''I'' = Δ''V''/Δ''I'' = ''R'' for any applied voltage or current or for the difference between any set of applied voltages or currents.

[[File:FourIVcurves.svg|thumb|400px|The [[Current–voltage characteristic|''I''–''V'' curve]]s of four devices: Two [[resistor]]s, a [[diode]], and a [[Battery (electricity)|battery]]. The two resistors follow Ohm's law: The plot is a straight line through the origin. The other two devices do ''not'' follow Ohm's law.]]

There are, however, components of electrical circuits which do not obey Ohm's law; that is, their relationship between current and voltage (their [[Current–voltage characteristic|''I''–''V'' curve]]) is ''nonlinear'' (or non-ohmic). An example is the [[Diode#Shockley diode equation|p–n junction diode]] (curve at right). As seen in the figure, the current does not increase linearly with applied voltage for a diode. One can determine a value of current (''I'') for a given value of applied voltage (''V'') from the curve, but not from Ohm's law, since the value of "resistance" is not constant as a function of applied voltage. Further, the current only increases significantly if the applied voltage is positive, not negative. The ratio ''V''/''I'' for some point along the nonlinear curve is sometimes called the ''static'', or ''chordal'', or [[direct current|DC]], resistance,<ref>{{cite book | title = Engineering System Dynamics | first = Forbes T.|last=Brown | publisher = CRC Press | year = 2006 | isbn = 978-0-8493-9648-9 | page = 43 | url = https://books.google.com/books?id=UzqX4j9VZWcC&q=%22chordal+resistance%22&pg=PA43 }}</ref><ref>{{cite book | title = Electromagnetic Compatibility Handbook | first = Kenneth L.|last=Kaiser | publisher = CRC Press | year = 2004 | isbn = 978-0-8493-2087-3 | pages = 13–52 | url = https://books.google.com/books?id=nZzOAsroBIEC&q=%22static+resistance%22+%22dynamic+resistance%22+nonlinear&pg=PT1031 }}</ref> but as seen in the figure the value of total {{math|''V''}} over total {{math|''I''}} varies depending on the particular point along the nonlinear curve which is chosen. This means the "DC resistance" V/I at some point on the curve is not the same as what would be determined by applying an AC signal having peak amplitude {{math|Δ''V''}} volts or {{math|Δ''I''}} amps centered at that same point along the curve and measuring {{math|Δ''V''/Δ''I''}}. However, in some diode applications, the AC signal applied to the device is small and it is possible to analyze the circuit in terms of the ''dynamic'', ''small-signal'', or ''incremental'' resistance, defined as the one over the slope of the ''V''–''I'' curve at the average value (DC operating point) of the voltage (that is, one over the [[derivative]] of current with respect to voltage). For sufficiently small signals, the dynamic resistance allows the Ohm's law small signal resistance to be calculated as approximately one over the slope of a line drawn tangentially to the ''V''–''I'' curve at the DC operating point.<ref name=horowitz-hill>{{cite book |last1=Horowitz |first1=Paul |author-link=Paul Horowitz |first2=Winfield|last2=Hill | title=The Art of Electronics |edition=2nd |year=1989 |publisher=Cambridge University Press |isbn=978-0-521-37095-0 |page = 13 | url = https://books.google.com/books?id=bkOMDgwFA28C&q=small-signal+%22dynamic+resistance%22&pg=PA13 |author2-link=Winfield Hill }}</ref>