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Questions and Answers
In circuit analysis, what is the defining characteristic of an 'essential node'?
In circuit analysis, what is the defining characteristic of an 'essential node'?
- It is a node where three or more circuit elements connect. (correct)
- It is a node with the highest voltage potential in the circuit.
- It is a point where exactly two circuit elements connect.
- It is a node connected to ground.
How does the number of essential nodes (ne) relate to the number of node-voltage equations needed to solve a circuit?
How does the number of essential nodes (ne) relate to the number of node-voltage equations needed to solve a circuit?
- The number of equations needed is equal to ne.
- The number of equations needed is independent of ne.
- The number of equations needed is equal to ne - 1. (correct)
- The number of equations needed is equal to ne + 1.
When applying the Node-Voltage method, what assumption is typically made about the direction of current flow at a node?
When applying the Node-Voltage method, what assumption is typically made about the direction of current flow at a node?
- Current is assumed to flow out of the node. (correct)
- Current is assumed to flow into the node.
- Current direction alternates between flowing in and out.
- The current direction is determined by the polarity of the voltage source.
How are dependent sources handled when applying the node-voltage method?
How are dependent sources handled when applying the node-voltage method?
What is a 'supernode' in the context of node-voltage analysis?
What is a 'supernode' in the context of node-voltage analysis?
Which of the following is true regarding a 'mesh current'?
Which of the following is true regarding a 'mesh current'?
In mesh analysis, how does the number of meshes in a circuit relate to the number of mesh-current equations required?
In mesh analysis, how does the number of meshes in a circuit relate to the number of mesh-current equations required?
When applying mesh analysis, what adjustments are needed if the circuit contains dependent sources?
When applying mesh analysis, what adjustments are needed if the circuit contains dependent sources?
Explain the concept of a 'supermesh' in mesh analysis.
Explain the concept of a 'supermesh' in mesh analysis.
What is the recommended approach when a circuit contains both a supernode and a supermesh?
What is the recommended approach when a circuit contains both a supernode and a supermesh?
Under what condition can a voltage source in series with a resistor be transformed into a current source?
Under what condition can a voltage source in series with a resistor be transformed into a current source?
What is the key property of the resistor when performing a source transformation?
What is the key property of the resistor when performing a source transformation?
In an electrical circuit, what is the purpose of finding the Thévenin equivalent?
In an electrical circuit, what is the purpose of finding the Thévenin equivalent?
What is the first step in determining the Thévenin equivalent of a circuit at terminals a-b?
What is the first step in determining the Thévenin equivalent of a circuit at terminals a-b?
How do you determine the Thévenin resistance (Rth) after finding the Thévenin voltage (Vth)?
How do you determine the Thévenin resistance (Rth) after finding the Thévenin voltage (Vth)?
What does the Norton equivalent circuit consist of?
What does the Norton equivalent circuit consist of?
How is the Norton current (In) determined when finding the Norton equivalent of a circuit?
How is the Norton current (In) determined when finding the Norton equivalent of a circuit?
How is the Norton resistance (Rn) related to the Thévenin resistance (Rth) for a given circuit?
How is the Norton resistance (Rn) related to the Thévenin resistance (Rth) for a given circuit?
What condition must be met for maximum power transfer to a load resistor (RL)?
What condition must be met for maximum power transfer to a load resistor (RL)?
Given a Thévenin equivalent circuit with VTh and RTh, what is the formula for calculating the maximum power that can be transferred to a load resistor RL?
Given a Thévenin equivalent circuit with VTh and RTh, what is the formula for calculating the maximum power that can be transferred to a load resistor RL?
If a circuit is composed of resistors and both independent and dependent sources, how do you determine the Thevenin resistance Rth?
If a circuit is composed of resistors and both independent and dependent sources, how do you determine the Thevenin resistance Rth?
When using superposition, what must you do with the independent sources in a circuit?
When using superposition, what must you do with the independent sources in a circuit?
What does 'deactivating' a voltage source mean when applying superposition?
What does 'deactivating' a voltage source mean when applying superposition?
In the context of superposition, what action is performed to 'deactivate' a current source?
In the context of superposition, what action is performed to 'deactivate' a current source?
Why is it important to not deactivate dependent sources when applying superposition?
Why is it important to not deactivate dependent sources when applying superposition?
When should the 'superposition' theorem be applied to circuit analysis?
When should the 'superposition' theorem be applied to circuit analysis?
What is the final step in applying the superposition theorem to a circuit?
What is the final step in applying the superposition theorem to a circuit?
If a circuit contains only resistors and dependent sources, what is the Thévenin voltage (VTh) at any terminal?
If a circuit contains only resistors and dependent sources, what is the Thévenin voltage (VTh) at any terminal?
If a circuit only contains resistors and dependent sources, how is the Thevenin resistance found?
If a circuit only contains resistors and dependent sources, how is the Thevenin resistance found?
How does circuit analysis aid in the design of systems for transferring power from a source to a load?
How does circuit analysis aid in the design of systems for transferring power from a source to a load?
In a circuit where the goal is to achieve maximum power transfer to a load, what relationship should exist between the load resistance ($R_L$) and the source impedance?
In a circuit where the goal is to achieve maximum power transfer to a load, what relationship should exist between the load resistance ($R_L$) and the source impedance?
In a purely resistive circuit, for what value of load resistance $R_L$ is the power transferred to the load maximized if the Thevenin equivalent resistance is $R_{Th}$?
In a purely resistive circuit, for what value of load resistance $R_L$ is the power transferred to the load maximized if the Thevenin equivalent resistance is $R_{Th}$?
When applying the superposition theorem, how does deactivating a voltage source affect the circuit?
When applying the superposition theorem, how does deactivating a voltage source affect the circuit?
Describe the effect of deactivating a current source when using the superposition theorem.
Describe the effect of deactivating a current source when using the superposition theorem.
When finding the Thevenin resistance ($R_{Th}$) of a circuit containing only resistors, where the independent voltage and current source are set to zero, what method is used?
When finding the Thevenin resistance ($R_{Th}$) of a circuit containing only resistors, where the independent voltage and current source are set to zero, what method is used?
What is the effect on the circuit if there are dependent sources in finding Thevenin resistance?
What is the effect on the circuit if there are dependent sources in finding Thevenin resistance?
What determines the maximum power transferred to a load?
What determines the maximum power transferred to a load?
Where electrical components are connected end-to-end to form a single path for current flow, what is this arrangement called?
Where electrical components are connected end-to-end to form a single path for current flow, what is this arrangement called?
Flashcards
What is a Node?
What is a Node?
A point where two or more circuit elements join.
What is an Essential Node?
What is an Essential Node?
A node where three or more circuit elements join.
What is a Path?
What is a Path?
A trace of adjoining basic elements with no elements included more than once.
What is a Branch?
What is a Branch?
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What is an Essential Branch?
What is an Essential Branch?
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What is a Loop?
What is a Loop?
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What is a Mesh?
What is a Mesh?
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What is Node-Voltage Method?
What is Node-Voltage Method?
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What is the current direction assumption in Node-Voltage analysis?
What is the current direction assumption in Node-Voltage analysis?
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What is Supernode?
What is Supernode?
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What is a mesh current?
What is a mesh current?
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What does the number of meshes equal?
What does the number of meshes equal?
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What is a SuperMesh?
What is a SuperMesh?
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Which method is preferred when there is a SuperNode?
Which method is preferred when there is a SuperNode?
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Which method is preferred when there is a SuperMesh?
Which method is preferred when there is a SuperMesh?
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What is Source Transformation?
What is Source Transformation?
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What should you omit?
What should you omit?
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What should you omit?
What should you omit?
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What is Thevenin Equivalent?
What is Thevenin Equivalent?
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What is Norton Equivalent?
What is Norton Equivalent?
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Describe Open-Circuit method
Describe Open-Circuit method
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Describe Short-Circuit method
Describe Short-Circuit method
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Describe Source Killer Method
Describe Source Killer Method
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What kind of sources do you not deactivate?
What kind of sources do you not deactivate?
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What is Superposition principle?
What is Superposition principle?
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Do not deactivate...
Do not deactivate...
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Describe Finding Rth
Describe Finding Rth
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When is maximum power transfer achieved?
When is maximum power transfer achieved?
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Study Notes
Terminology
- A node is a point where two or more circuit elements join. In Figure 4.3, nodes are labeled a, b, c, d, e, f and g.
- An essential node is a node where three or more circuit elements join. In Figure 4.3, essential nodes are b, c, e, and g.
- A path is a trace of adjoining basic circuit elements with no elements included more than once.
- A branch is a path that connects two nodes.
- An essential branch is a path that connects two essential nodes without passing through another essential node.
- A loop is a path whose last node is the same as the starting node: V1 - R1 - R5 - R6 - R4 - V2.
- A mesh is a loop that does not enclose any other loops: V1 - R1 - R5 - R3 - R2.
Introduction to the Node-Voltage Method
- For a circuit with 'ne' essential nodes, 'ne - 1' node-voltage equations are needed. With 3 essential nodes you need 2 equations.
- Voltages are referenced to a non-reference essential node.
- Node-voltage equations involve taking KCL at certain nodes.
- Current is assumed to flow out of the node.
Node-Voltage
- KCL applies to Node 1 with the formula ia + ib + ic = 0.
- Terms can be rewritten as:
- ia = (v1-10)/1
- ib = v1/5
- ic = (v1-v2)/2
- v1(1/1 + 1/5 + 1/2) - 10 - v2(1/2) = 0. Simplified: 1.7v1 - 0.5v2 = 10
- Apply KCL to Node 2
- (v2-v1)/2 + v2/10 - 2 = 0. Simplified: -0.5v2 + 0.6v1 = 2
- Solving the two equations with two unknowns yields v1 = 9.09V, v2 = 10.091V
The Node-Voltage Method and Dependent Sources
- If the circuit contains dependent sources, the node-voltage equations need to be supplemented with constraint equations from dependent sources
- For the sample circuit, the node-voltage equation is -3 + (vo-0)/200 + (vo-(-5iΔ))/10 + (vo-80)/20 = 3
- iΔ = (v0-80)/20
- Solving: v0 = 50V
The Node-Voltage Method: Some Special Cases
- For a circuit with a known node-voltage, like v1=100V, only one additional node-voltage equation is needed.
- Supernode: When a voltage source is between two essential nodes, combine the two nodes to form a supernode.
- From the positive to the negative terminal: v3 - v2 = 20. Note that v1 = 50V
Introduction to the Mesh-Current Method
- A mesh current exists only in the perimeter of a mesh.
- The number of mesh equations equals the number of meshes.
Mesh-Current
- KCL and KVL equations can be used to find the currents i1, i2, and i3.
- Alternatively, mesh-current equations:
- i1 = ia
- i2 = ib
- i3 = ia - ib
- Mesh#1: -v1 + R1ia + R3(ia-ib) = 0
- Mesh#2: R2ib + v2 + R3(ib-ia) = 0
The Mesh-Current Method and Dependent Sources
- If the circuit contains dependent sources, the mesh-current equations must be supplemented with constraint equations.
- iø = ia - ic
The Mesh-Current Method: Some Special Cases
- If there is a known mesh current, like ia=20 A, we need two mesh equations.
- SuperMesh is formed when a current source is between two meshes.
SuperMesh Equations
- SuperMesh (a + c): -100 + 3(ia – ib) + 2(ic – ib) + 50 + 4ic + 6ia = 0
- The SuperMesh Equation: ic - ia = 5
- Mesh (b): 10ib + 2(ib – ic) + 3(ib – ia) = 0
The Node-Voltage Method vs. the Mesh-Current Method
- If there is a SuperNode, use the Node-Voltage method.
- If there is a SuperMesh, use the Mesh-Current method.
SuperPosition
-
When a linear system is excited by more than one independent source, the total response is the sum of the individual responses.
-
Applying SuperPosition
-
Deactivate all independent sources except one. Do not deactivate dependent sources:
- An independent voltage source is short-circuited
- An independent current source is open-circuited
-
Find response v'
-
Repeat the process for other sources to find v", as needed.
-
The total response equals the sum of the individual responses: v=v'+v"+v"'.
Source Transformation
- Transform a voltage source in series with a resistor to a current source in parallel using the same resistor.
- Transform a current source in parallel with a resistor to a voltage source in series with the same resistor.
- Equation Vs / R
- If there is a resistor Rp in parallel with the voltage source, remove it prior to transforming
- If there is a resistor Rs in series with the current source, remove it prior to transforming
Thevenin Equivalent
- An independent voltage source Vth is in series with a resistor Rth. They are used to describe the behavior of a terminal.
- Open-circuit the terminals a−b to find Voc = Vth
- Short-circuit the terminals a−b to find Rth: Rth = Vth / Isc
Norton Equivalent
- An independent current source IN is in parallel with a resistor RN
- Short-circuit at terminals a-b to find IN.
- Open-circuit at terminals a-b to find determine RN: VN = Voc / IN.
- The Norton equivalent circuit is simply the source transformation of a Thevenin equivalent circuit
Finding Rth
- Kill all independent sources:
- Short circuiting Voltage source
- Open circuiting Current source Find the equivalent resistance between node a-b If there are dependent sources in the circuit, apply a voltage test (VT)
- Rth = VT/IT
Applying Kill-Source and Test-Source Methods to Find RTη
- In circuits with only resistors and independent sources: Use the Kill-Source Method; Req = RTh
- For resistors, dependent sources, and independent sources short circuit: Use the Short-Circuit Method and that current, Rτη = VTh / Isc .
- Resistors and only dependent sources use the Test-Source method, RTh = VT / IT.
Maximum Power Transfer
- Maximum power transfer occurs when RL = RTh.
- Equation for maximum power: Pмах = vTh squared divided by 4RL.
- The equation with Norton equivalent circuit that can be written as equation PMax = 1/4*IN squared RL
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