Circuit Theory Question KCL and Dependent Sources?

In summary: Pick one, and label it as Vx. Then you know what the voltage is for the other node. You can then use KCL to get an equation with your two unknowns.In summary, the problem is to find the voltages and currents in a circuit, with a focus on finding Io. The student knows that they need to use KCL, but is unsure how to proceed. They provide an attempt at a solution, but there is an error in their equation and they are unsure how to find another equation. The expert suggests identifying two voltage nodes and using KCL to obtain an equation with the two unknowns, Io and Vx.
  • #1
Jose F Gomez D
6
0

Homework Statement


I need to find the voltages (if any) and currents of these circuit, but particularly Io
I do know that I have to use KCL bot I don't know how, can somebody help me with a node or somethinghttps://www.physicsforums.com/attachments/c2-jpg.80412/

I do not have any other info apart from this image

Homework Equations



C2.jpg

KCL

The Attempt at a Solution



I don't know how to tackle this problem
I think by KCL

-Io = -I(Vx)+5A-3Vx

but not sure

and how do I find Vx? is
Vx=I(5 amp)*R(4 ohm)=5*4=20 volts ?

then the dependent current is 3*20=60 volts? but is current it should be on ampere not volt

or should I solve the resistors and get Req
1/ (1/(8+4)+1/6) = 4 ohm = Req

C2.jpg


there is one node on the top and another one on the bottom, but that one is ground, so shoul I transform the current source and the Io resistor into a voltage source?
 
Last edited by a moderator:
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  • #2
Why don't you try applying KCL yourself and show us what you get. Note that providing an attempt is mandatory according to forum rules, we need to see where/if you go wrong to help you properly with your understanding.
 
  • #3
Jose F Gomez D said:

Homework Statement


I need to find the voltages (if any) and currents of these circuit, but particularly Io
I do know that I have to use KCL bot I don't know how, can somebody help me with a node or somethinghttps://www.physicsforums.com/attachments/c2-jpg.80412/

I do not have any other info apart from this image

Homework Equations



View attachment 80414
KCL

The Attempt at a Solution



I don't know how to tackle this problem
I think by KCL

-Io = -I(Vx)+5A-3Vx

but not sure

and how do I find Vx? is
Vx=I(5 amp)*R(4 ohm)=5*4=20 volts ?

then the dependent current is 3*20=60 volts? but is current it should be on ampere not volt

or should I solve the resistors and get Req
1/ (1/(8+4)+1/6) = 4 ohm = Req

View attachment 80414

there is one node on the top and another one on the bottom, but that one is ground, so shoul I transform the current source and the Io resistor into a voltage source?
you are on the right track

-Io = -I(Vx)+5A-3Vx There is an error in this equation.

Remember that in most cases you must have one equation for every unknown.
This implies that you might have to apply Kirchhoff's laws one more time (seeing as there are two unknowns).
 
Last edited by a moderator:
  • #4
donpacino said:
you are on the right track

-Io = -I(Vx)+5A-3Vx There is an error in this equation.

Remember that in most cases you must have one equation for every unknown.
This implies that you might have to apply Kirchhoff's laws one more time (seeing as there are two unknowns).

so my node is 5 (the current source) = Io (the one I need to find) + 3Vx (the one with the dependent source) + I1 (the one with the 8 and 4 resistances)

5=Io+3Vx+I1

I1=Vt/12
Vt=V(in 4)+V(in 8)
Vt=Vx+2Vx
Vt = 3 Vx

I1 = Vx/4

my unknowns are Io and Vx,

5=Io+3Vx+Vx/4

I really have no clue where is the other equation
 
  • #5
Jose F Gomez D said:
so my node is 5 (the current source) = Io (the one I need to find) + 3Vx (the one with the dependent source) + I1 (the one with the 8 and 4 resistances)

5=Io+3Vx+I1

I1=Vt/12
Vt=V(in 4)+V(in 8)
Vt=Vx+2Vx
Vt = 3 Vx

I1 = Vx/4

my unknowns are Io and Vx,

5=Io+3Vx+Vx/4

I really have no clue where is the other equation
I see 3 voltage nodes. If you reference one as ground, the other two are unknown.
 

1. What is Kirchhoff's Current Law (KCL)?

Kirchhoff's Current Law (KCL) states that the algebraic sum of currents entering and exiting a node (or junction) in a circuit is equal to zero. In other words, the total current flowing into a node must be equal to the total current flowing out of the node.

2. How can KCL be used to solve circuit problems?

KCL can be used to analyze complex circuits by breaking them down into smaller, simpler parts. By applying KCL at each node in the circuit, we can write and solve a set of equations to determine the current flowing through each element in the circuit.

3. What is a dependent source in circuit theory?

A dependent source is a circuit element whose value depends on the voltage or current in another part of the circuit. This type of source is commonly used in circuit analysis to model behavior such as amplification or feedback.

4. How are dependent sources represented in circuit diagrams?

Dependent sources are typically represented by diamond-shaped symbols, with the dependent variable indicated inside the diamond. For example, a voltage-controlled voltage source would be represented as a diamond with a "V" inside, while a current-controlled current source would be represented with a "I" inside.

5. Can dependent sources be used in KCL equations?

Yes, dependent sources can be used in KCL equations just like any other circuit element. Their values can be determined by substituting the appropriate voltage or current value from the controlling element into the KCL equation at the relevant node.

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