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Questions and Answers
When determining the Thevenin equivalent resistance ($R_T$) across terminals A and B of a circuit, under what condition must the terminals be?
When determining the Thevenin equivalent resistance ($R_T$) across terminals A and B of a circuit, under what condition must the terminals be?
- The terminals must be connected to a load resistance equal to the expected $R_T$ value.
- The terminals must be connected to a voltage source equal to the expected Thevenin voltage.
- The terminals must be open-circuited. (correct)
- The terminals must be short-circuited.
In Thevenin's theorem, what is the significance of $V_{OC}$ (open-circuit voltage) when determining the Thevenin equivalent circuit?
In Thevenin's theorem, what is the significance of $V_{OC}$ (open-circuit voltage) when determining the Thevenin equivalent circuit?
- It equals the Thevenin equivalent voltage ($V_T$). (correct)
- It represents the voltage across the shorted terminals A and B.
- It is always zero, simplifying the calculation.
- It's used to calculate the equivalent resistance ($R_T$).
What is the primary characteristic that defines a 'mesh' in the context of mesh analysis?
What is the primary characteristic that defines a 'mesh' in the context of mesh analysis?
- A mesh is the outermost loop of a circuit.
- A mesh is a closed path containing multiple loops.
- A mesh is a loop that does not contain any other loops within it. (correct)
- A mesh is any closed path in a circuit.
What principle is directly applied when performing mesh analysis on a circuit?
What principle is directly applied when performing mesh analysis on a circuit?
In mesh analysis, what does the term 'element constraints' refer to?
In mesh analysis, what does the term 'element constraints' refer to?
What is the significance of the polarity of voltage sources when applying the 'direct method' for mesh analysis?
What is the significance of the polarity of voltage sources when applying the 'direct method' for mesh analysis?
In using the 'direct method' for mesh analysis, what does setting the sum of the voltages opposing any loop to zero achieve?
In using the 'direct method' for mesh analysis, what does setting the sum of the voltages opposing any loop to zero achieve?
Using mesh current equations by inspection, what do $R_{XY}$ terms signify?
Using mesh current equations by inspection, what do $R_{XY}$ terms signify?
According to mesh analysis equations by inspection, what do the terms $\Sigma v_X$ represent?
According to mesh analysis equations by inspection, what do the terms $\Sigma v_X$ represent?
When using mesh analysis by inspection, what is a key limitation regarding the types of circuits to which this method can be applied?
When using mesh analysis by inspection, what is a key limitation regarding the types of circuits to which this method can be applied?
If the current $i_A$ in mesh A is calculated as -0.6757mA, how should this result be interpreted?
If the current $i_A$ in mesh A is calculated as -0.6757mA, how should this result be interpreted?
When setting up mesh equations by inspection, what should be taken into account when including voltage sources?
When setting up mesh equations by inspection, what should be taken into account when including voltage sources?
What adjustments need to be made to apply mesh analysis to a circuit containing current sources?
What adjustments need to be made to apply mesh analysis to a circuit containing current sources?
How are dependent (controlled) sources handled differently from independent sources when writing mesh equations?
How are dependent (controlled) sources handled differently from independent sources when writing mesh equations?
In a circuit with multiple meshes, if you calculate a mesh current to be zero, what does this imply?
In a circuit with multiple meshes, if you calculate a mesh current to be zero, what does this imply?
When utilizing mesh analysis, how does increasing the number of meshes within a circuit typically affect the complexity of the calculations?
When utilizing mesh analysis, how does increasing the number of meshes within a circuit typically affect the complexity of the calculations?
In the context of circuit analysis, what is the primary benefit of using matrix notation to solve mesh current equations?
In the context of circuit analysis, what is the primary benefit of using matrix notation to solve mesh current equations?
Why is it important to be consistent with the assumed direction of mesh currents during mesh analysis?
Why is it important to be consistent with the assumed direction of mesh currents during mesh analysis?
What is one practical implication of accurately performing mesh analysis (i.e., why do engineers care about this)?
What is one practical implication of accurately performing mesh analysis (i.e., why do engineers care about this)?
In what way does the principle of linearity relate to the applicability and accuracy of mesh analysis?
In what way does the principle of linearity relate to the applicability and accuracy of mesh analysis?
Flashcards
What is a 'mesh' in circuit analysis?
What is a 'mesh' in circuit analysis?
A loop which does not contain any other loop within it.
What's the first step in Mesh analysis?
What's the first step in Mesh analysis?
Apply Kirchhoff's Voltage Law (KVL) around each mesh in the circuit.
What is the direct method in mesh analysis?
What is the direct method in mesh analysis?
Write the KVL equation for each mesh by summing the voltages, ensuring the current opposes the mesh current.
What does the direct method rely on?
What does the direct method rely on?
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What is the final goal with Mesh Analysis?
What is the final goal with Mesh Analysis?
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Mesh current equations by inspection?
Mesh current equations by inspection?
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When to use Mesh equation inspection?
When to use Mesh equation inspection?
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Study Notes
- Lecture 8 covers Circuit analysis
- Department of Computer Engineering
- UET (Lahore)
Circuit Reduction - Exercise 3-28
- Find the Thevenin equivalent at nodes A and B
- Given circuit contains multiple resistors and a voltage source
- With 1.5 kΩ, 2.2 kΩ, 4.7 kΩ, 10 kΩ, and 3.3 kΩ resistors
- Furthermore a 5V voltage Source is present
- Thevenin equivalent voltage (VT) = 4.14 V
- Thevenin equivalent resistance (RT) = 5.01 kΩ
Calculating Thevenin Equivalent
- Assuming that VC = 0, then VD = -5V
- Apply direct method at Node B to the open circuit (AB)
- (vB - (-5))/3.7K + (vB - (-5))/4.7K + (vB - 0)/10K = 0 resulting in vB ≈ -4.14V
- VT = VOC = VAB = VCB = VC - VB = 0 - (-4.14) = 4.14V
- After using the direct method at Node B for the short circuit (AB), with UB - (-5) /3.7K + (UB - (-5))/4.7K + (UB - 0)/10K + (UB - 0)/3.3K = 0 resulting in vB ≈ -2.73V
- iN = iSC = (vC - vB)/3.3K ≈ 0.826mA
- RT = VT/iN ≈ 5.01kΩ
Mesh Current Analysis (Mesh Analysis)
- A mesh is a loop that does not contain any other loop; it is the boundary of a "window pane" in the circuit.
- Each mesh has its own current.
- The goal is to find the current of each mesh.
Mesh Analysis of a Linear Circuit Without Current Sources
- Write Kirchhoff's Voltage Law (KVL) around each mesh, followed by element constraints.
- For Example 1: Calculate iA and iB
- KVL for Mesh A: -v4 + v1 + v3 = 0
- KVL for Mesh B: -v3 + v2 + v5 = 0
- Element constraints for Mesh A: -12 + (iA)6K + (iA - iB)6K = 0
- Element constraints for Mesh B: -(iA - iB)6K + (iB)3K + 3 = 0
- Solving simultaneously, iA = 5/4 mA and iB = 1/2 mA
Example 2:
- The goal is to calculate iA, iB, and iC
- KVL for Mesh A: -v2 + v4 - v5 = 0
- KVL for Mesh B: -v1 + v2 + v3 = 0
- KVL for Mesh C: -v3 + v5 + v6 = 0
- Element constraints for Mesh A: -(-6) + (iA)4K - (iC - iA)6K = 0
- Element constraints for Mesh B: -(iB)9K - 6 + (iB - iC)3K = 0
- Element constraints for Mesh C: -(iB - iC)3K + (iC - iA)6K - (iC)12K = 0
- Solving simultaneously, iA = -0.6757mA, iB = 0.4685mA, and iC = -0.1261mA
Direct Method for Writing Mesh Current Equations
- It's a shortcut for writing the mesh current equations.
- The sum of the voltages opposing any loop is 0; the + and - symbols for each element in the mesh are made to oppose the mesh current.
- For Example 2, rewritten:
- Mesh A: (iA)4K + (iA - iC)6K + 6 = 0
- Mesh B: (iB)9K + 6 + (iB - iC)3K = 0
- Mesh C: (iC - iB)3K + (iC - iA)6K + (iC)12K = 0
- After solving simultaneously iA = -0.6757mA, iB = 0.4685mA ic = -0.1261mA
- For Example 1, rewritten:
- Mesh A: -12 + (iA)6K + (iA - iB)6K = 0
- Mesh B: (iB - iA)6K + (iB)3K + 3 = 0
- After solving simultaneously iA = 5/4 mA, iB = 1/2 mA
Mesh Current Equations by Inspection
- applicable to linear circuits without current sources.
- ΣRx = sum of resistances in mesh X.
- ΣRxy = sum of resistances common to mesh X and mesh Y.
- Σvx = sum of source voltages favoring mesh X.
- Given the provided formula and matrix notation for calculating mesh currents, for Example 1 it can be expressed as:
- 6K + 6K -6K iA
- −6K 6K+3K)(iB = 12
- By converting into matrix form and solving, iA = 5/4 and iB = 1/2
- Example 2 can be revisited and shown as: [4K + 6K -0 -6K][iA]
- 0 9K + 3K -3K iB -6 +6
- -6K -3K 3K+6K +12K][ic -0
- By using the formula and converting into the matrix form, the result will be iA= -0.6757m, iB = 0.4685m, and iC = -0.1261m
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