Thévenin's theorem represents a linear electrical network viewed through two terminals by a voltage source in series with a resistance. Its mathematical content
is the reduction of the network's linear equations to an affine
terminal relation. When that relation has a well-defined finite open-circuit voltage
and resistance 
, it can be written
 |
where 
is the current delivered from the positive-voltage terminal to an external load.
Here 
is the voltage at 
,
and 
is the slope of the terminal relation (Massachusetts Institute of Technology 2011).
For a passive resistor network, 
is nonnegative. It can
be found by suppressing independent voltage sources to short circuits and independent
current sources to open circuits. Dependent sources must remain active; a test voltage
or current then determines the terminal resistance. Active networks can have negative
, and singular networks need not
admit this finite representation.
A load resistance 
has terminal voltage 
,
so
 |
provided the denominator is nonzero. For finite nonzero 
, the equivalent parallel-current-source description is
given by Norton's theorem, with current 
.
