Dependent current source, find Vo

In summary: And I agree with your logic that the current through the two "parallel" resistors will be the same. They are parallel only in the sense that they are both connected to the same node.)In summary, to find the voltage V0 in the given network, the resistors can be simplified to 4k ohm each. Using the current division rule, the current through the right branch is found to be 6 mA. Therefore, V0 can be calculated using V = IR, giving a final answer of 36V.
  • #1
Color_of_Cyan
386
0

Homework Statement



http://imageshack.us/a/img26/4592/homeworkprintprob.jpg Find the voltage V0 in the network.

Homework Equations



V = IR

Voltage Division:
(Voltage across series resistor) = [(resistance) / total series resistance)](total input V)

Current Division (for 2 parallel resistors):
(current across parallel resistor) = [(other resistor) / (sum of parallel resistors)](total incoming current)]

The Attempt at a Solution



I can simplify the 1k and 3k resistors to 4k no matter what.

I'm not sure if I can simplify the 6k and 12k on the bottom as parallel though, but they will be 4k.

4k + 4k + 2k in series becomes 10k, assuming you can do that with the current source.

Then 10k + 6k makes

R total = 16k ohm, and then I tot = 24 mA

V = IR means Vtot = 384V.

Then voltage division would make

V0 = [ (6k)/(6k+10k) ](384V) = 144V

would this be correct?
 
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  • #2
Color_of_Cyan said:
I can simplify the 1k and 3k resistors to 4k no matter what.

I'm not sure if I can simplify the 6k and 12k on the bottom as parallel though, but they will be 4k.
Yes, okay so far.
4k + 4k + 2k in series becomes 10k, assuming you can do that with the current source.
Nope. Can't do that. There are separate paths with separate currents; there's a loop to the left of the current source and a loop to the right of the current source. The current will be different in the two loops. You might think about using the current division rule to see how much of the 24mA from the source flows in each loop...
 
  • #3
Why don't you draw a simpler schematic?

You said the 12 and 6 make 4. The 3 and 1 make 4. The 2 and 6 make 8. So draw it with those 3 resistances and see what you can make of it.

BTW, it's not a dependent current source, it's a constant current source.
 
  • #4
I can simplify the 1k and 3k resistors to 4k no matter what.

I'm not sure if I can simplify the 6k and 12k on the bottom as parallel though, but they will be 4k.

What others have said. OK so far.

If you redraw the circuit at this point you should see that a further simplification can be made.

Should be possible to treat it as a current divider at that point.
 
  • #5
I got confused and thought you could simplify the resistors in series like that since it was a constant current source, heh. Never mind then. 384V seemed way too high too.
So then: :

http://img835.imageshack.us/img835/7570/homeworkprintprobedit.jpg and then doing current division:

Current through right branch = (4k/16k)(24 mA) = 6 mA

and then V knot is just V = IR, since current is the same through parallel elements

V knot = (6 mA)(6 kΩ) = 36VThanks.
 
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  • #6
That's what I make it.
 

FAQ: Dependent current source, find Vo

1. What is a dependent current source?

A dependent current source is an electrical component that provides a current output that is dependent on a voltage or current elsewhere in the circuit. It is denoted by a diamond-shaped symbol with a circle or arrow inside, and is used to model current sources in electronic circuits.

2. How does a dependent current source work?

A dependent current source works by controlling the current output based on the voltage or current at a specified location in the circuit. This can be achieved through the use of a control voltage or current, which is typically denoted by a letter such as V or I, and a coefficient or multiplier value that determines the relationship between the control signal and the output current.

3. What is the difference between a dependent and independent current source?

The main difference between a dependent and independent current source is that an independent current source provides a fixed current output regardless of the circuit conditions, while a dependent current source's output is determined by the voltage or current at a specific location in the circuit.

4. How do you find Vo in a circuit with a dependent current source?

To find Vo in a circuit with a dependent current source, you will need to use Ohm's Law and Kirchoff's Laws to analyze the circuit and determine the relationship between the dependent current source's control signal and the output voltage. Once this relationship is established, you can use algebraic equations to solve for the value of Vo.

5. What are some applications of dependent current sources?

Dependent current sources are commonly used in electronic circuits to model and control current sources, such as in voltage regulators, amplifiers, and power supplies. They can also be used in simulation software to accurately model real-world circuits and their behaviors.

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