Original Circuit Prior to the Thévénin Equivalent
Thévénin Equivalent
The Thévénin voltage is the open circuit voltage at the output. calculation is
straightforward node or loop circuit analysis. Using loop analysis:
V_{oc}: [8 * I1] + [(8+2+6) * I2]  [6 * I3] =
1 A
I2 = ½A ==> Voc = ½A * 6
Ω= 3 V = V_{th}
Calculate the Thévénin resistance from the open circuit voltage and the short
circuit current
(set R_{L} = 0 and solve for I3) using Ohm's Law.
R_{th} = V_{oc} / I_{sc} = 3 V / [(4/9)
A] = 27 / 4 Ω = R_{th}
The Thévénin Equivalent of a circuit consists of a Thévénin voltage source in
series with a Thévénin resistor and is valid for any load. In AC circuits a Thévénin
equivalent circuit is valid for a single frequency.
 See Full List 
Thévénin's Theorem
Thévénin's Theorem is a fundamental concept in electrical engineering that
simplifies complex linear electrical networks into simpler, equivalent circuits.
It's named after the French engineer Léon Charles Thévénin, who formulated the
theorem. Thévénin's Theorem is particularly useful for analyzing and solving
circuits with multiple components and sources.
The theorem states that any linear electrical network with multiple sources
and resistive elements can be replaced by a single voltage source (Thévénin
voltage) in series with a single resistor (Thévénin resistance). This simplified
equivalent circuit is called the Thévénin equivalent circuit.
Here are the key components of the Thévénin equivalent circuit:
 Thévénin Voltage (V_{th}): The Thévénin voltage (V_{th}) is the opencircuit
voltage measured across the two terminals of interest in the original circuit
after all the independent voltage sources have been replaced with short circuits
and all the independent current sources have been replaced with open circuits.
In other words, Vth is the voltage you would measure between the two terminals
when no load is connected.
 Thévénin Resistance (R_{th}): The Thévénin resistance (R_{th}) is the equivalent
resistance measured across the same two terminals in the original circuit, again
with all independent sources turned off (replaced with their internal
resistances, if any). To calculate R_{th}, you remove the sources and determine the
equivalent resistance seen from the terminals.
The Thévénin equivalent circuit consists of a single voltage source V_{th} in
series with a single resistor R_{th}. This equivalent circuit can accurately
represent the behavior of the original circuit as seen from the terminals of
interest, making it easier to analyze and solve complex circuits. It is
especially valuable when you want to determine how a particular load will affect
the voltage and current at the terminals without delving into the entire
circuit.
To find the Thévénin voltage and resistance, you typically follow these
steps:
 Turn off all independent voltage sources (replace with short circuits) and
all independent current sources (replace with open circuits).
 Calculate the voltage across the two terminals of interest (Vth) in the
simplified circuit.
 Calculate the equivalent resistance (Rth) between the two terminals.
 Construct the Thévénin equivalent circuit with Vth and Rth in series.
Once you have the Thévénin equivalent circuit, you can use it to analyze the
behavior of the original circuit when connected to various loads or to simplify
circuit analysis for complex networks.
Posted September 8, 2023 (updated from original
post on
6/30/2001)
