Finding a voltage in a circuit with only resistors and current sources

In summary, the problem at hand is to find V0 in a circuit using Kirchhoff's Current and Voltage Laws. The attempt at a solution involved writing a node equation and assuming the voltage across certain resistors. However, there is confusion on how to proceed and whether to find the current in certain branches or the voltages across the current sources. The suggestion is to rewrite the node equation without referencing Vx and Vy for the resistive branches, and then substitute expressions for Vx and Vy for the controlled source terms.
  • #1
Deluxe489
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Homework Statement


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Find V0 in the circuit.

Homework Equations


Kirchhoff's Current Law: All currents entering a node must sum to zero.
Kirchhoff's Voltage Law: All voltages around a loop must sum to zero.

The Attempt at a Solution



So far, I have taken the top of the center branch to be a node with five currents entering/leaving it. Using Kirchhoff's Current Law, I have done:

0 = 2Vy + (3Vx / 3Ω) + 6A - (2Vy / 4Ω) - 4Vx

I assumed that the voltage across the 2Ω resistor in the second branch from the right was also Vy, and I assumed that the voltage across the 2Ω resistor in the second branch from the left was 2Vx. I know this because I know that the current is constant within each branch.

Solving the equation for Vx, I got:

Vx = (1/2)Vy + 2A

At this point, though, I'm confused about what to do. I've thought of using Kirchhoff's Voltage Law using the loop formed by the two resistor branches (so basically ignoring all the branches that current sources in them), but even if I do that and make the substitution I derived from Kirchhoff's Current Law, I don't know how I'm supposed to get V0 from doing that. Am I supposed to find the current in those two branches and then just add up the voltage drops across the four resistors? If so, I'm not sure how to find the currents. Am I supposed to find the voltages across the current sources?

I would really appreciate any help.

Thank you.
 
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  • #2
It would, perhaps, be easier to first write the node equation without reference to Vx or Vy except for their controlled source contributions. Then separately write expressions for Vx and Vy in terms of Vo and substitute them into the node equation later. As it stands, I don't understand your terms for the resistor branches. Surely the current in the 1Ω + 2Ω branch would be =Vx/1Ω ?

Anyways. Try writing the equation without referencing Vx and Vy for the resistive branches. Afterwards substitute expressions for Vx and Vy for the controlled source terms.
 

FAQ: Finding a voltage in a circuit with only resistors and current sources

1. How do I calculate the voltage in a circuit with only resistors and current sources?

The voltage in a circuit with only resistors and current sources can be calculated using Ohm's Law, which states that voltage (V) is equal to current (I) multiplied by resistance (R). In other words, V = I * R. Simply plug in the values of the current and resistance in the circuit to solve for voltage.

2. Can I use Kirchhoff's Laws to find the voltage in this type of circuit?

Yes, you can use Kirchhoff's Laws to find the voltage in a circuit with only resistors and current sources. Kirchhoff's Voltage Law (KVL) states that the sum of all voltage drops in a closed loop must equal the sum of all voltage sources in the loop. By applying KVL to the circuit, you can find the voltage across each component.

3. What are some common techniques for finding the voltage in this type of circuit?

In addition to using Ohm's Law and Kirchhoff's Laws, some other common techniques for finding voltage in a circuit with only resistors and current sources include using voltage dividers, mesh analysis, and nodal analysis. These techniques can be useful in more complex circuits with multiple components.

4. Can the voltage in this type of circuit change over time?

In a circuit with only resistors and current sources, the voltage will remain constant over time as long as the current sources remain constant. However, if the current sources vary, then the voltage in the circuit will also vary accordingly. Additionally, the voltage may also change if there are any changes in the resistance values in the circuit.

5. How does the placement of the current sources affect the voltage in the circuit?

The placement of current sources in a circuit with only resistors and current sources does not affect the overall voltage in the circuit. The voltage across each component will depend on the individual current and resistance values, regardless of where the current sources are placed. However, the placement of the current sources may affect the direction of the current flow in the circuit.

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