Electrical Engineering: Thevenin's Theorem

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Questions and Answers

What is the first step in finding the Thevenin resistance (Rth)?

Turning off the 32-V voltage source and the 2-A current source

What is the total resistance in the circuit when finding Rth?

4Ω

What is the formula to find Vth?

Vth = 12i1 - i2

What is the value of i2 in the circuit?

-2A Signup and view all the answers

What is the value of i1 in the circuit?

0.5A Signup and view all the answers

What is the value of Vth in the circuit?

30V Signup and view all the answers

What is the current through the load resistor (RL) when RL = 6Ω?

3A Signup and view all the answers

What is the purpose of Thevenin's theorem?

To find the equivalent circuit to the left of the terminals in a given circuit Signup and view all the answers

Why was Thevenin's theorem developed?

To avoid the need to reanalyze a circuit every time a variable element is changed. Signup and view all the answers

What is the purpose of Thevenin's equivalent circuit?

To replace the fixed part of a circuit with a simpler equivalent circuit. Signup and view all the answers

What is the case 1 procedure for finding Thevenin's equivalent circuit?

Turn off all independent sources, and find the input resistance Rth of the network looking between terminals a and b. Signup and view all the answers

What is another way to determine the value of a specific variable in a circuit with two or more independent sources?

Using the superposition principle Signup and view all the answers

What is the case 2 procedure for finding Thevenin's equivalent circuit?

Apply a voltage source vo at terminals a and b, and find the resulting current io, or apply a current source io at terminals a-b and find the terminal voltage vo. Signup and view all the answers

What property of a circuit is necessary for the superposition principle to apply?

Linearity Signup and view all the answers

What is the formula for finding the load voltage VL?

VL = IL RL = (Vth / (Rth + RL)) Signup and view all the answers

What is the first step when applying the superposition theorem?

Turn off all independent sources except one source Signup and view all the answers

What is the formula for finding the load current IL?

IL = Vth / (Rth + RL) Signup and view all the answers

How do we find the total contribution when applying the superposition theorem?

By adding algebraically all the contributions due to the independent sources Signup and view all the answers

What is the purpose of finding Thevenin's equivalent circuit in a network?

To simplify the analysis of a circuit and find the voltage and current at a particular load. Signup and view all the answers

What is the purpose of turning off all independent sources except one when applying the superposition theorem?

To find the contribution of each independent source to the variable Signup and view all the answers

What is the advantage of using Thevenin's theorem in circuit analysis?

It allows for the simplification of a complex circuit and reduces the need to reanalyze the circuit every time a variable element is changed. Signup and view all the answers

What is the equation for finding the total voltage in a circuit with two independent sources using the superposition theorem?

$v = v1 + v2$ Signup and view all the answers

What is the method used to find $v1$ in the example circuit?

Voltage division or KVL Signup and view all the answers

What is the final answer for $v$ in the example circuit?

2V Signup and view all the answers

What is the current $i_3$ in the circuit using current division?

2A Signup and view all the answers

What is the voltage $v_2$ in the circuit using Ohm's law?

8V Signup and view all the answers

What is the output voltage $v_o$ in the circuit using superposition theorem?

10V Signup and view all the answers

What is Norton's theorem used for in circuit analysis?

Replacing a linear two-terminal circuit with an equivalent circuit consisting of a current source and a resistor. Signup and view all the answers

What is the relationship between the Norton resistance $R_N$ and Thevenin resistance $R_{Th}$?

They are equal, $R_N = R_{Th}$ Signup and view all the answers

How do you find the Norton current $I_N$ in a circuit?

By determining the short-circuit current flowing from terminal a to b. Signup and view all the answers

What is the Norton equivalent circuit of the circuit in Fig. below at terminals a-b?

A current source $I_N$ in parallel with a resistor $R_N$ Signup and view all the answers

What are the values of $I_N$ and $R_N$ in the circuit in Fig. below at terminals a-b?

$I_N = 4.5A$ and $R_N = 90\Omega$ Signup and view all the answers

Study Notes

Network Theorems

Thevenin's Theorem

Developed to simplify circuit analysis when a variable load is present
Allows replacement of a fixed part of a circuit with an equivalent circuit
Thevenin's equivalent circuit consists of a voltage source (Vth) and a resistance (Rth) in series

Calculating Rth and Vth

Case 1: No dependent sources
- Turn off all independent sources
- Rth is the input resistance of the network looking between terminals a and b
Case 2: Dependent sources present
- Turn off all independent sources
- Apply a voltage source vo at terminals a and b and determine the resulting current io
- Rth = vo / io
- Alternatively, insert a current source io at terminals a-b and find the terminal voltage vo

Important Formulas

Vth = Rth * IL / (Rth + RL)
IL = Vth / (Rth + RL)

Example: Finding Thevenin Equivalent Circuit

Steps:
1. Find Rth by turning off the voltage source and current source
2. Calculate Vth by finding the voltage across the load resistor
3. Redraw the circuit as an equivalent Thevenin circuit

Superposition Theorem

If a circuit has two or more independent sources, one way to determine the value of a specific variable (voltage or current) is to use nodal or mesh analysis
Another way is to determine the contribution of each independent source to the variable and then add them up
Steps to take when applying the superposition theorem:
1. Turn off all independent sources except one source
2. Find the output (voltage or current) due to that active source
3. Repeat step 1 for each of the other independent sources
4. Find the total contribution by adding algebraically all the contributions due to the independent sources

Example: Using Superposition Theorem

Steps:
1. Set the current source to zero and find v1
2. Set the voltage source to zero and find v2
3. Apply the superposition theorem to find v = v1 + v2

Norton's Theorem

States that a linear two-terminal circuit can be replaced by an equivalent circuit consisting of a current source IN in parallel with a resistor RN
IN is the short-circuit current through the terminals
RN is the input or equivalent resistance at the terminals when the independent sources are turned off

Norton's Equivalent Circuit

RN = RTH
IN = short-circuit current flowing from terminal a to b

Example: Finding Norton Equivalent Circuit

Steps:
1. Find RN in the same way as RTH
2. Find IN by determining the short-circuit current flowing from terminal a to b

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Description

Understand Thevenin's theorem, its development, and its application in equivalent circuits. Learn how it's used to analyze circuits with variable loads.