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Thevenin’s theorem states that any linear circuit, irrespective of how complicated, can be simplified to an equivalent circuit with a single voltage source and a resistance in series.
- Generally, Ohm’s law and Kirchhoff’s law are used to solve complex electrical circuits.
- However many circuit analysis theorems are used to solve complex circuit problems.
- Among them, Thevenin’s theorem is most commonly used.
- According to this, any complex circuit containing a number of resistances and voltage sources can be simplified to an equivalent circuit with a single voltage source and a series resistance.
- Thevenin’s theorem is used in the analysis of power systems.
Also Read: Ohm’s Law
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Key Terms: Electric, Electricity Current, Resistance, Resistor, Ohm, Ohms Law, Voltage, Thevenin’s theorem, Equivalent resistance, Voltage
What Is Thevenin Theorem?
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According to Thevenin's theorem, any linear circuit, regardless of its complexity, can be reduced to an equivalent circuit consisting of a single voltage source in series with a single resistance.
- This equivalent circuit is known as the Thevenin equivalent circuit.
- The voltage of the Thevenin equivalent circuit is known as Thevenin voltage, denoted by VTH.
- The equivalent resistance is known as Thevenin’s resistance, denoted by RTH.
Also Read: Cells, emf, Internal Resistance
Applications Of Thevenin Theorem
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The applications of Thevenin's theorem are:
- Thevenin’s theorem is used for analyzing power systems.
- Thevenin’s theorem is useful in source modeling and resistance measurement using the Wheatstone bridge.
Also Read:
| Important Topics Based On Thevenin Theorem | ||
|---|---|---|
| Network Analysis | Resistors In Parallel Formula | Current Electricity |
| Electrical Current | Electric Current | Electric Current and Circuit |
How to Use Thevenin Theorem?
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The following are the procedure to convert a given network into Thevenin’s equivalent circuit
- Remove the load resistor from the original circuit and calculate the voltage across the open connection to determine the Thevenin source voltage (VTH).
- Remove all power sources from the original circuit (voltage sources shorted and current sources open) and calculate the total resistance between open connection points to determine the Thevenin resistance (RTH).
- Draw the Thevenin's equivalent circuit by connecting the Thevenin voltage source to the Thevenin resistance and load resistance.
- Find the voltage or current across the load resistor.
\(I_L=\frac{V_{TH}}{R_{TH}+R_L}\)
Limitations Of Thevenin Theorem
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The limitations of the Thevenin theorem are:
- Thevenin’s theorem can only be used in the analysis of linear circuits.
- The power dissipation of the Thevenin equivalent is not identical to the power dissipation of the entire system.
Also Read: Electric Circuit
Advantage Of Thevenin Theorem
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The advantages of the Thevenin theorem are:
- Thevenin theorem is used to determine the current of a specific segment of the network. The resistance of segments of vares whereas other resistances and e.m.f sources are constant.
- Thevenin theorem reduces the complex circuit to a single circuit via a single source of e.m.f. The Eth is in a series with a single resistance Rth.
Solved Examples
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Ques: Draw Thevenin’s equivalent circuit and find the voltage across RL, for the given circuit:
To convert the given circuit into Thevenin's equivalent circuit, first, remove the load resistance and calculate the equivalent resistance in the circuit, as shown in the figure
Now the load resistance is in series with the equivalent resistance, then net resistance is given by
Rnet = Req + RL
Rnet = 4 + 2 = 6Ω
Hence the current in the circuit is given by Ohm’s law V = IRnet
Therefore I = V/Rnet = 10/6 = 1.66 A
The voltage across the load resistance is given by
VL = IRL = 1.66 x 2 = 3.33 V
Also Read:
| Chapter Related Topics | ||
|---|---|---|
| Types of Circuits | Types of Resistors | Unit of Voltage |
| Resistors in Series and Parallel Combination | Equivalent Resistance Formula | Difference Between Series and Parallel Circuits |
Things To Remember
- The value of e is the open circuit voltage at the terminals.
- The value of r is e divided by the current with the terminals short-circuited.
- Thevenin’s theorem is used in the analysis of linear circuits.
- Thevenin’s theorem is used for analyzing power systems.
- Thevenin theorem reduces the complex circuit to a single circuit
Sample Questions
Ques. Is Thevenin’s theorem applicable to AC circuits? (1 Mark)
Ans. Thevenin’s theorem does not apply to AC circuits which consist of linear elements like resistors, inductors, and capacitors.
Ques. What is the basic application of the Thevenin theorem? (1 Mark)
Ans. Thevenin theorem is essentially used in circuit analysis, power system analysis, and short circuit calculations and is a key tool for circuit design.
Ques. Calculate the Vth for the following given circuit. (1 Mark)
(a) 3.33V
(b) 6.66V
(c) 3.37V
(d) 6.67V
Ans. 6.67V
Explanation: 4 ohms are removed and then v across 2 ohms is calculated by the voltage divider.
2 ✕ 10/(2+1) = 6.67V
Ques. Define Thevenin's theorem. (1.5 Marks)
Ans. Thevenin theorem is defined as any combination of batteries and resistances with two terminals that can be replaced by a single voltage source e and a single series resistor r. The value of e is the open circuit voltage at the terminals, and the value of r is e divided by the current with the terminals short-circuited.
Ques. State the advantages of the Thevenin theorem. (2 Marks)
Ans. The advantages of the Thevenin theorem are:
- Thevenin theorem is used to determine the current of a specific segment of the network. The resistance of segments of vares whereas other resistances and e.m.f sources are constant.
- Thevenin theorem reduces the complex circuit to a single circuit via a single source of e.m.f. The Eth is in a series with a single resistance Rth.
Ques. Is Thevenin’s theorem applicable to non-linear circuits? (1 Mark)
Ans. No, Thevenin’s theorem is not applicable to non-linear circuits.
Ques. What are the limitations of Thevenin's theorem? (1.5 Marks)
Ans. The limitations of the Thevenin theorem are:
- Thevenin’s theorem can only be used in the analysis of linear circuits.
- The power dissipation of the Thevenin equivalent is not identical to the power dissipation of the whole system.
Ques. Calculate the Thevenin resistance across the terminal AB for the following circuit. (1 Mark)
(a) 2.32 ohm
(b) 3.43 ohm
(c) 3.67 ohm
(d) 4.34 ohm
Ans. 3.67 ohm
Explanation: The Thevenin resistance is found by opening the circuit between the specified terminal and shorting all voltage sources.
In 10V source we get;
Rth = (1| | 2)+3 = 3.67 ohm
Ques. Where is Thevenin’s theorem used? (1 Mark)
Ans. Thevenin’s theorem is used for the analysis of power systems.
Ques. List the usage of the Thevenin theorem. (1 Mark)
Ans. The uses of the Thevenin theorem is:
- Thevenin’s theorem is used for analysing the power systems.
- Thevenin’s theorem is useful in source modelling and resistance measurement using the Wheatstone bridge.
Also Read:
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