Thevenin theorem

“Any linear circuit involving numerous voltages and resistances can be replaced by just one single voltage in series with a single resistance connected across the load,” according to Thevenin’s Theorem. To put it another way, any electrical circuit, no matter how complicated, can be reduced to a two-terminal equivalent using only a single constant voltage source in series with a resistance (or impedance) coupled to a load.

Ohm’s law

The three most essential components of electricity are voltage, current, and resistance. The link between these three variables is depicted by Ohm’s law. The current flowing through a conductor between two points is proportional to the voltage across the conductor, according to Ohm’s law.

According to Ohm’s law:

V α R

🡺V=IR

Here, V is the voltage or potential difference across resistor R and I is the current flowing through the resistor.

Applications of Ohm’s law

Ohm’s law can be used to determine the voltage, current, impedance, or resistance of a linear electric circuit when the other two quantities are known.

Ohm’s Law’s main applications include:

• It makes power calculations easier.
• Ohm’s law is used to maintain the desired voltage drop between the electrical components.
• The voltage, resistance, and current of an electric circuit must all be determined.
• Ohm’s law is also used in DC ammeters and other DC shunts to divert current.

Limitations of Ohm’s law

1. Unilateral networks are exempt from the Ohm’s law. In unilateral networks, current can only flow in one way. These networks make use of diodes, transistors, and other electronic components.
2. Ohm’s law does not apply to non-linear components. The current of non-linear components is not proportional to the applied voltage, implying that the resistance of those elements’ changes with voltage and current. Non-linear elements, such as the thyristor, provide an example.

Thevenin’s theorem

According to Thevenin’s Theorem, any sophisticated network can be replaced by a voltage source with one resistance in series across its load terminals. When the resistance of a branch is changed while the rest of the network remains the same, this theorem aids in the analysis of current variation in that branch.

Steps to be followed in order to apply Thevenin’s theorem

1. Remove the load resistor from the original circuit and calculate the voltage across the open connection points where the load resistor was to find the Thevenin source voltage.
2. Remove all power sources from the original circuit (voltage sources are shorted and current sources are open) and calculate total resistance between the open connection points to find the Thevenin resistance.
3. Create the Thevenin equivalent circuit by connecting the Thevenin voltage source to the Thevenin resistance. The load resistor reconnects between the analogous circuit’s two open terminals.
4. Analyse the load resistor’s voltage and current using the series circuit principles.

Applying Thevenin’s theorem in a DC circuit

Let us consider the above DC circuit for applying Thevenin’s theorem.

We will be measuring the current flowing through the 40 resistor.

To begin analysing the circuit, we must first remove the central 40-ohm load resistor connected across terminals A-B, as well as any internal voltage source resistance (s). This is accomplished by shorting out all of the circuit’s voltage sources, resulting in v = 0, or by open circuiting any associated current sources, resulting in I = 0. The reason for this is that for circuit analysis, we need an ideal voltage source or an ideal current source.

Calculating the equivalent resistance looking back from the terminals A and B with all the voltage sources shorted yields the equivalent resistance, RS. The circuit after that is as follows.

The equivalent resistance will be: RS=10×2010+20=6.67

Now, we will calculate the equivalent voltage.

The current flowing through the circuit will be:

I=VR

🡺I=20-1010+20=0.33A

Voltage across AB will be: 

VAB=20-20×0.33=13.33V
Now, the Thevenin equivalent circuit will be:

Therefore, the current flowing through the 40 resistor will be:

I=VR

🡺I=13.3346.67=0.286A

Applications of Thevenin’s theorem

• Thevenin’s theorem is used in power system analysis.
• Thevenin’s theorem is utilised in source modelling and Wheatstone bridge resistance measurement.

Limitations of Thevenin theorem

• Only linear circuits are subjected to Thevenin’s theorem.
• The power loss of the Thevenin equivalent is not the same as the real system’s power dissipation.

Conclusion

While Thevenin’s circuit theorem can be expressed mathematically in terms of current and voltage, it is less powerful in larger networks than Mesh Current Analysis or Nodal Voltage Analysis. However, Mesh or Nodal analysis is usually required in any Thevenin exercise, so it might as well be used right away. Thevenin’s equivalent circuits of transistors, voltage sources such as batteries, and other components, on the other hand, are extremely valuable in circuit design.