Thevenin's Theorem Questions

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Very Short Answers Questions [1 Mark Questions]

Ques. Who derived Thevenin’s Theorem?

Ans. The German physicist Hermann von Helmholtz initially established the theorem in 1853, but history remembered the French engineer Leon Thevenin, who proposed a more elegant way to prove the theorem in 1883.

Ques. What is Thevenin Voltage?

Ans. Thevenin voltage is an open-circuit voltage that is obtained by removing the load resistance with an open circuit and measuring the potential difference across the terminals.

Ques. What is the application of Thevenin’s Theorem?

Ans. The main application of Thevenin’s theorem is to obtain the voltage and current across the load of a power system.

Ques. Can Thevenin’s Theorem be applied to AC circuits?

Ans. Yes, Thevenin's theorem may be used for both AC and DC circuits. But this theorem is only applicable to circuits containing linear elements like resistors, inductors, and capacitors.

Ques. What is Thevenin’s resistance?

Ans. Thevenin’s resistance is an equivalent series resistance obtained from simplifying the complex linear circuits using Thevenin’s Theorem.

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Short Answers Questions [2 Marks Questions]

Ques. State Thevenin’s Theorem.

Ans. According to Thevenin’s Theorem, it is possible to simplify any linear electric circuit to an equivalent electric circuit consisting of one voltage source known as Thevenin’s voltage and an equivalent resistance known as Thevenin’s resistance connected in series with it, no matter how complex the circuit is.

Ques. What are the theoretical limitations of Thevenin’s Theorem?

Ans. The theoretical limitation of Thevenin’s theorem is that it can only be used in the analysis of linear circuits. In electrical circuits having magnetic coupling between the load and any other circuit component, this theorem is not applicable.

Ques. Is it possible to simplify any complex linear circuits?

Ans. Yes, any complex linear circuits can be simplified by using Thevenin’s Theorem. With the help of this theorem, the complex circuit can be converted into a circuit containing a single voltage source with a resistance in series.

Ques. Give a few examples of network analysis theorems.

Ans. A few examples of network analysis theorems are

• Superposition Theorem
• Thevenin’s Theorem
• Norton’s Theorem
• Maximum Power Transfer Theorem

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Long Answers Questions [3 Marks Questions]

Ques. What are the practical limitations of Thevenin’s Theorem?

Ans. The practical limitations of Thevenin’s Theorem are

• The linearity of many electrical circuits is limited to a particular range of values. Thevenin's Theorem is thus limited to this linear range.

• Thevenin’s equivalent has equivalent V-I characteristics only when viewed from the load resistance.

• The power dissipation of the Thevenin equivalent is not exactly the same as that of the actual system. However, irrespective of the internal resistance, the power dissipated between two output terminals by an external resistor remains the same.

Ques. Compare Thevenin’s Theorem and Norton’s Theorem.

Ans. The comparison between Thevenin’s Theorem and Norton’s Theorem is given below

• The equivalent circuit obtained from Thevenin’s Theorem contains a voltage source while the equivalent circuit obtained from Norton’s Theorem contains a current source.
• The equivalent circuit from Thevenin’s theorem has a resistor in series with the source, while the equivalent circuit from Norton’s theorem has a resistor in parallel with the source.
• Thevenin’s resistance and Norton’s resistance have the same value.
• Norton’s theorem can easily be derived from Thevenin’s theorem.

Ques. What are the steps to follow Thevenin’s Theorem?

Ans. The steps followed to analyze a circuit using Thevenin's Theorem are

• The first step is to remove the load resistance and measure the open circuit voltage across the opened points.
• This open circuit voltage is known as the Thevenin’s voltage.
• Now replaced the voltage source with a short circuit and the current source with an open circuit.
• The resistance of the circuit is calculated and this equivalent resistance is known as Thevenin’s resistance.
• The next step is to draw a circuit in which Thevenin’s resistance is kept in series with the Thevenin’s voltage
• Using the laws of series electrical circuits analyze current and voltage for the load resistor.

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Very Long Answers Questions [5 Marks Questions]

Ques. Find Thevenin voltage (V_TH), Thevenin resistance (R_TH), and the load current I_L flowing through and load voltage (V_L) across the load resistor in the given figure using Thevenin's Theorem.

Ans. To measure the Thevenin voltage V_TH the load resistance R_L = 5 kΩ is removed. Hence the circuit becomes an open circuit.

Now the open circuit voltage is equal to the voltage across the 4 kΩ resistor. Hence the current in the circuit is given by

I = 48/(12 + 4) = 3 x 10^-3 A

Therefore, the Thevenin voltage is given by

V_TH = 4 kΩ x 3 x 10^-3 A = 12 V

Now to calculate the Thevenin’s resistance (R_TH), we have short the voltage source

Thevenin resistance, R_TH = [12 || 4] + 8 = [(12 x 4)/(12 + 4)] + 8

⇒ R_TH = 3 + 8 = 11 kΩ

Thevenin’s equivalent circuit is given by

The current through the load resistance is given by

I_L = V_TH / (R_TH + R_L) = 12 / (11 + 5) = 0.75 mA

Also, Voltage across load resistance is given by

V_L = I_L x R_L = 0.75 mA x 5 kΩ = 3.75 V

Ques. Calculate the current through the resistor of resistance 6 Ω.

Ans. Removed the load resistance 6 Ω. The circuit becomes an open circuit.=

The open circuit voltage is equal to the voltage across the 4 Ω resistor. Hence the current in the circuit is given by

I = 6 / (4 + 2) = 1 A

Therefore, the Thevenin’s voltage, V_TH = 4 x 1 = 4 V

Now short the voltage source to find the Thevenin’s resistance R_TH

R_TH = [2 || 4] + 2 = 3.34 Ω

Thevenin’s equivalent circuit is given by

The current through the load resistance is given by

I_L = 4 / (3.34 + 6) = 0.43 A

Ques. Calculate the Thevenin’s voltage and Thevenin’s resistance

Ans. In this case, the open circuit voltage is equal to the voltage across the 7 Ω resistance. Hence, the current in the circuit is given by

I = 12 / (3 + 7 + 2) = 12 / 12 = 1 A

Therefore, Thevenin’s voltage is given by

⇒ V_TH = 7 x 1 = 7 V

To calculate Thevenin’s resistance, the voltage source is short-circuited.

Thevenin’s resistance, R_TH = [(3 + 2) || 7] + 3 + 3

⇒ R_TH = [5 || 7] + 6 = [(5 x 7) / (5 + 7)] + 6

⇒ R_TH = (35/12) + 6 = 8.92 Ω

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