= Thévenin terminal response
{c}
{title2=$V=V_{\mathrm{oc}}-IR_{\mathrm{th}}$}
With the <passive sign convention> applied to the network, its entering <electric current> is $J=-I$, and the same relation becomes $V=V_{\mathrm{oc}}+JR_{\mathrm{th}}$. The <electrical load> uses the <passive sign convention> with entering <electric current> $I$, so it absorbs <power> $VI$. A positive delivered <electric current> therefore produces a voltage drop for positive $R_{\mathrm{th}}$; changing the reference direction without changing the equation would give the wrong sign.
The reason is <linearity> of <Ohm's law>, <Kirchhoff's current law>, <Kirchhoff's voltage law>, and the constitutive relations of any linear <dependent electrical sources>. Solve once at $I=0$ with the <independent electrical sources> present. Subtract this solution from a solution with prescribed delivered <electric current> $I$: the fixed <independent electrical sources> cancel, leaving a homogeneous <linear> network whose terminal voltage change is proportional to $I$. This is a short <superposition principle> argument for an <affine function>; the fixed offset need not vanish.
The qualification about a well-defined response matters. An ideal <voltage source> alone has $R_{\mathrm{th}}=0$. An ideal nonzero <current source> alone constrains $I$ and does not have a finite open-circuit voltage or a representation $V=V_{\mathrm{oc}}-IR_{\mathrm{th}}$ with finite coefficients. Linear <dependent electrical sources> can give <negative resistance>, and singular ideal networks may fail to have a unique finite response. Neither a finite nor a strictly positive passive $R_{\mathrm{th}}$ follows merely from calling an <electrical circuit> linear. <Thevenin and Norton Equivalents, University of Houston teaching notes>[Thevenin and Norton Equivalents, p. 11, “On a Negative Thevenin Equivalent Resistance”: dependent-source models can have negative equivalent resistance]{ref}
Back to article page
