What is Thevenin’s theorem?

Any linear circuit, no matter how complex, maybe simplified to an equivalent circuit utilizing only a single voltage source and series resistance coupled to a load, according to Thevenin's Theorem. The superposition principle says that all foundational equations must be linear, and the notion of "linear" is still the same (i.e., there should not be any exponentials or roots). This is particularly the case when operating with passive elements like resistors, inductors, and capacitors. However, some components (particularly some gaseous and semiconductor devices like tunnel diode, Schottky diode, transistors like BJT, MOSFET) are nonlinear, meaning their current resistance fluctuates with voltage and current. As a result, circuits made up of these parts are known as nonlinear circuits.

What is the principle of Thevenin’s theorem?

Thevenin's theorem is a path to lessen a network to a voltage source, branch resistance, and load equivalent circuit of only one source.

Follow these steps to prove Thevenin's Theorem:

• The load resistor is detached from the circuit given in the question. The open voltage from one terminal of the load resistor to the other terminal is computed to determine the Thevenin voltage.
• All independent sources (independent voltage sources and independent current sources) are deactivated from the circuit given in the question. The equivalent resistance from one terminal of the load resistor to the other terminal is computed to determine the Thevenin resistance. To deactivate independent voltage sources, remove the voltage source and short circuit the branch containing it. To deactivate independent current sources, remove the current source and  open the circuit of the branch containing it.
• The Thevenin equivalent voltage and Thevenin equivalent resistance obtained are then combined in series. This connection is then combined with the load resistor to complete the circuit, forming the Thevenin circuit.
• Applying basic circuit solving methods and KVL (Kirchoff's voltage law) will result in the required voltage and current through the load resistor.

Thevenin’s voltage

The voltage is determined between the two points where the load resistor was previously connected. To do so, use any analytical tools you have at your fingertips. We can enforce the principles of series circuits, Ohm's law, and Kirchhoff's voltage law to compute the voltage all over the open load terminals. The circuit given in the question with the load resistor eliminated is simply a series circuit with competing batteries.

Thevenin’s series resistance

All independent sources (independent voltage sources and independent current sources) are deactivated from the circuit given in the question to determine the Thevenin resistance of the simplified circuit. And the equivalent resistance from one terminal of the load resistor to the other terminal is computed. To deactivate independent voltage sources, remove the voltage source and short circuit the branch containing it. To deactivate independent current sources, remove the current source and open the circuit of the branch containing it. 

Thevenin’s equivalent circuit

Thevenin's theorem simplifies this by temporarily suspending the resistive load from the original circuit and condensing what's left to an identical circuit consisting of one voltage source and adjoining resistance. The load resistance is then attached to obtain Thevenin equivalent circuit, and calculations are undertaken as if the entire network were a closed-loop (solving as KVL):

If correctly derived, the Thevenin simplified circuit will function exactly like the original circuit constructed by $B_1, R_1, R_3, \mathrm{and} B_2$ and the thevenin simplified circuit of $E_{thevenin} \mathrm{and} R_{thevenin}$.

Of course, the "Thevenin transformation" to the simplified circuit has the advantage of making load voltage and load current considerably faster and more efficient to solve than they were in the initial connection. Computing the matching Thevenin supply voltage and resistance is rather straightforward.

Below is another example showing a complete solution to network solving using the Thevenin theorem.

Uses of the Thevenin theorem

• To forecast the range of load voltage fluctuation owing to a change in load resistance, determine the change in load voltage
• To find the analogous circuit of Norton's circuit
• To establish the highest volume of electricity that can be transported from the network to the load

Common Mistakes

Remember that the Thevenin theorem is valid for linear and bilateral circuits containing only passive elements, i.e., resistors, capacitors, and inductors. Thevenin voltage can only be found across the load terminals of the circuit given.

Context and Applications

In each of the expert exams for undergraduate and graduate publications, this topic is huge and is mainly used in the following context:

• Bachelor of technology in the Electrical and Electronics Department
• Bachelor of Science in Physics
• Master of Science in Physics

Related Concepts

• Norton theorem
• Superposition theorem
• Helmholtz-Thevenin theorem and gas-discharging property

Practice Problems

Q1. $V_{TH}$ can be found across which part of the network?

(a) Output

(b) Input

(c) Both of the above mentioned

(d) None of these

Correct option- (a)

Explanation- According to Thevenin's theorem, $V_{TH}$ is not found across the input terminals but the output terminals, i.e., on the load side.

Q2. Which theorem is considered Thevenin's theorem's dual?

(a) Norton's theorem

(b) Reciprocity theorem

(c) Compensation theorem

(d) Millman's theorem

Correct option- (a)

Explanation- Norton's theorem is considered a dual of Thevenin's theorem because short circuit current is incorporated as a calculating parameter in Norton theorem, a dual of open-circuit voltage, which is used as a calculating parameter for Thevenin theorem.

Q3. Is it possible to apply Thevenin's theorem to a circuit consisting of a MOSFET?

(a) Yes

(b) No

(c) Depends on the MOSFET

(d) Data missing

Correct option- (b)

Explanation- Only linear networks can benefit from Thevenin's theorem. Because MOSFET is not a linear network, we can't use Thevenin's theorem to solve it.

Q4. What are valid networks for Thevenin's theorem?

(a)  Non-linear

(b) Linear

(c) Both

(d) None of these

Correct option- (b)

Explanation-Only linear networks are valid for the Thevenin theorem as they show no sign of abrupt voltage or current gains like transistors.

Q5. The Thevenin resistance so obtained __________ compared to Norton resistance.

(a) twice

(b) thrice

(c) quadruples

(d) remains the same

Correct option- (d)

Explanation- The Thevenin resistance and Norton resistance are the same for the same circuit. Also, they both are calculated using the same method as described above. Only Thevenin voltage and Norton current are computed differently.