Thevenin Theorem
Thevenin Theorem
It provides a mathematical technique for replacing for a given network, as viewed from two output terminals by a single voltage source with a series resistance. It makes the solution of complicated networks (particularly, electronic networks) quite quick and easy.
The Thevenin’s theorem, as applied to d.c. circuits, may be stated as under:
The current flowing through a load resistance RL connected across any two terminals A and B of a linear, active bilateral network is given by VOC || (Ri + RL) where VOC is the open-circuit voltage (i.e. voltage across the two terminals when RL is removed) and Ri is the internal resistance of the network as viewed back into the open-circuited network from terminals A and B with all voltage sources replaced by their internal resistance (if any) and current sources by infinite resistance.
How to Thevenize a given circuit?
1. Temporarily remove the resistance (called load resistance RL) whose current is required.
2. Find an open-circuit voltage VOC which appears across the two terminals from where resistance has been removed. It is also called the Thevenin voltage Vth.
3. Compute the resistance of the whose network as looked into from these two terminals after all voltage sources have been removed by living behind their internal resistances (if any) and current sources have been replaced by open-circuit i.e. infinite resistance. It is also called Thevenin resistance Rth or Ri.
4. Replace the entire network by a single Thevenin source, whose voltage is Vth or Voc and whose internal resistance is Rth or Ri.
5. Connect RL back to its terminals from where it was previously removed.
6. Finally calculate the current flowing through RL by using the equation,
I = Vth / (Rth + RL) or I = Voc / (Ri + RL)
Example 1
Convert the circuit shown in Figure (a), to a single voltage source in series with a single resistor.
Solution
Obviously, we have to find the equivalent circuit. For this purpose, we have to calculate
It provides a mathematical technique for replacing for a given network, as viewed from two output terminals by a single voltage source with a series resistance. It makes the solution of complicated networks (particularly, electronic networks) quite quick and easy.
The Thevenin’s theorem, as applied to d.c. circuits, may be stated as under:
The current flowing through a load resistance RL connected across any two terminals A and B of a linear, active bilateral network is given by VOC || (Ri + RL) where VOC is the open-circuit voltage (i.e. voltage across the two terminals when RL is removed) and Ri is the internal resistance of the network as viewed back into the open-circuited network from terminals A and B with all voltage sources replaced by their internal resistance (if any) and current sources by infinite resistance.
How to Thevenize a given circuit?
1. Temporarily remove the resistance (called load resistance RL) whose current is required.
2. Find an open-circuit voltage VOC which appears across the two terminals from where resistance has been removed. It is also called the Thevenin voltage Vth.
3. Compute the resistance of the whose network as looked into from these two terminals after all voltage sources have been removed by living behind their internal resistances (if any) and current sources have been replaced by open-circuit i.e. infinite resistance. It is also called Thevenin resistance Rth or Ri.
4. Replace the entire network by a single Thevenin source, whose voltage is Vth or Voc and whose internal resistance is Rth or Ri.
5. Connect RL back to its terminals from where it was previously removed.
6. Finally calculate the current flowing through RL by using the equation,
I = Vth / (Rth + RL) or I = Voc / (Ri + RL)
Example 1
Convert the circuit shown in Figure (a), to a single voltage source in series with a single resistor.
Solution
Obviously, we have to find the equivalent circuit. For this purpose, we have to calculate
References: Electrical Circuits by Charles S. Siskind http://tcmosul.net/files/pages/page_2691799140226070238.pdf