Solve Vo: Voltage Nodal Analysis w/ KCL Equation

In summary: So, when you write the KCL equation for the node at Vb, the voltage source will have a negative sign in the equation. This will result in a negative coefficient for the term Vb in your KCL equation. So, when you solve the equation for Vb, you will get a negative value. In summary, when using nodal analysis to solve for Vo in the given equation, the dependent voltage source 20iΔ will have a negative coefficient in the KCL equation for the node at Vb, resulting in a negative value for Vb when solved.
  • #1
elhaxx
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1566725276772.png

I'm asked to solve for Vo for this equation. I've set the bottom node to be my reference node before applying nodal analysis. When included in the KCL equation for node at Vb, will the dependent voltage source 20iΔ be negative since the current through that element is leaving node C?
Say, the equation would be: [(Vb-10v)/10Ω]+ (Vb/40Ω)+[(Vb+20iΔ)/20Ω]=0
Thanks!
 
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  • #2
I moved this to the homework forum. Please post homework questions to a homework forum and fill out the required information.
 
  • #3
elhaxx said:
When included in the KCL equation for node at Vb, will the dependent voltage source 20iΔ be negative since the current through that element is leaving node C?

–20iΔ is the voltage Vc

(typo corrected)
 
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  • #4
Welcome to the PF.
elhaxx said:
I'm asked to solve for Vo for this equation.
I see Va, Vb, Vc labeled, but no Vo label. Which voltage are you supposed to solve for? Thanks.
 
  • #5
berkeman said:
Welcome to the PF.

I see Va, Vb, Vc labeled, but no Vo label. Which voltage are you supposed to solve for? Thanks.
Vo = Vb, labeled across the 40ohm resistor.
 
  • #6
Your equation looks good to me. The voltage at node Vc is negative because of the polarity of the dependent source, as labeled in the schematic.
 
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1. What is voltage nodal analysis?

Voltage nodal analysis is a method used in circuit analysis to determine the voltage at each node (connection point) in a circuit. It involves applying Kirchhoff's Current Law (KCL) to each node to create a set of equations that can be solved to find the unknown node voltages.

2. How is KCL used in voltage nodal analysis?

Kirchhoff's Current Law states that the algebraic sum of currents entering and leaving a node must be equal to zero. In voltage nodal analysis, this law is used to create a set of equations for each node in a circuit, where the sum of the currents entering the node equals the sum of the currents leaving the node.

3. What are the steps for solving a circuit using voltage nodal analysis?

The steps for solving a circuit using voltage nodal analysis are:

  1. Identify all the nodes in the circuit and label them.
  2. Select a reference node and assign it a voltage of 0.
  3. Apply KCL to each node, creating a set of equations.
  4. Substitute known values and solve the equations to find the unknown node voltages.
  5. Verify the solution by checking that the sum of currents at each node is equal to zero and that the voltages across all components are consistent with the calculated node voltages.

4. What are the limitations of voltage nodal analysis?

Voltage nodal analysis is limited to circuits that can be represented as a series of nodes connected by branches. It also assumes that the circuit is in steady state, meaning that all voltages and currents are constant over time. Additionally, it is not suitable for circuits with non-linear components or dependent sources.

5. How is voltage nodal analysis different from other circuit analysis methods?

Voltage nodal analysis is different from other methods, such as mesh analysis or Thevenin's theorem, because it focuses on the individual nodes in a circuit rather than the individual loops or equivalent circuits. It also takes into account the current entering and leaving each node, rather than the voltage drops across components or the equivalent resistance of a circuit.

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