32 Questions
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
What is the value of i1 in the circuit?
0.5A
What is the value of Vth in the circuit?
30V
What is the current through the load resistor (RL) when RL = 6Ω?
3A
What is the purpose of Thevenin's theorem?
To find the equivalent circuit to the left of the terminals in a given circuit
Why was Thevenin's theorem developed?
To avoid the need to reanalyze a circuit every time a variable element is changed.
What is the purpose of Thevenin's equivalent circuit?
To replace the fixed part of a circuit with a simpler equivalent circuit.
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.
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
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.
What property of a circuit is necessary for the superposition principle to apply?
Linearity
What is the formula for finding the load voltage VL?
VL = IL RL = (Vth / (Rth + RL))
What is the first step when applying the superposition theorem?
Turn off all independent sources except one source
What is the formula for finding the load current IL?
IL = Vth / (Rth + RL)
How do we find the total contribution when applying the superposition theorem?
By adding algebraically all the contributions due to the independent sources
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.
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
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.
What is the equation for finding the total voltage in a circuit with two independent sources using the superposition theorem?
$v = v1 + v2$
What is the method used to find $v1$ in the example circuit?
Voltage division or KVL
What is the final answer for $v$ in the example circuit?
2V
What is the current $i_3$ in the circuit using current division?
2A
What is the voltage $v_2$ in the circuit using Ohm's law?
8V
What is the output voltage $v_o$ in the circuit using superposition theorem?
10V
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.
What is the relationship between the Norton resistance $R_N$ and Thevenin resistance $R_{Th}$?
They are equal, $R_N = R_{Th}$
How do you find the Norton current $I_N$ in a circuit?
By determining the short-circuit current flowing from terminal a to b.
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 $R_N$
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 $R_N = 90\Omega$
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:
- Find Rth by turning off the voltage source and current source
- Calculate Vth by finding the voltage across the load resistor
- 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:
- Turn off all independent sources except one source
- Find the output (voltage or current) due to that active source
- Repeat step 1 for each of the other independent sources
- Find the total contribution by adding algebraically all the contributions due to the independent sources
Example: Using Superposition Theorem
- Steps:
- Set the current source to zero and find v1
- Set the voltage source to zero and find v2
- 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:
- Find RN in the same way as RTH
- Find IN by determining the short-circuit current flowing from terminal a to b
Understand Thevenin's theorem, its development, and its application in equivalent circuits. Learn how it's used to analyze circuits with variable loads.
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