Power Analysis in Circuits: Understanding the Flow of Current

In summary, the conversation revolves around using different methods to solve for V_out in a circuit. The methods discussed include using Kirchhoff's Laws, mesh analysis, and the Superposition Theorem. The final answer for V_out is -4.2308V, which is a negative value. The conversation also briefly touches on determining the power produced by each voltage source, which can be calculated using the equation P=IV. The direction of current flow in relation to the positive or negative terminal of a voltage source determines whether the power is positive or negative.
  • #1
charlies1902
162
0
I attached the circuit. I'm trying to solve for V_out, but I'm stuck.
I can solve for it using mesh analysis, but there must be an easier way. I just don't see it yet. Can anyone give me a hint?
 

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  • #2
charlies1902 said:
I attached the circuit. I'm trying to solve for V_out, but I'm stuck.
I can solve for it using mesh analysis, but there must be an easier way. I just don't see it yet. Can anyone give me a hint?
attachment.php?attachmentid=55191&d=1359520682.png

Use Kirchhoff's Laws.

I don't know that it's any easier than mesh analysis.
 
  • #3
To me simplest seems using the Superposition Theorem.
 
  • #4
SammyS said:
attachment.php?attachmentid=55191&d=1359520682.png

Use Kirchhoff's Laws.

I don't know that it's any easier than mesh analysis.

I used mesh analysis. Can someone verify if my answer at the bottom is correct?

Here's what I did using mesh analysis:
1. For the 3 closed loops, assume each loop has a clockwise current
2. I1 is the left loop's current, I2 is the middle, and I3 is the right

Given:
R1=1000Ω R2=2000Ω R3=3000Ω R4=4000Ω
V1=V3=10V, V2=5V

For loop 1 (left):
-1000*I_1-10=0
-1000*I_1=10

For loop 2 (mid):
10-2000I2-3000I2+3000I3=0
-5000I+3000I3=-10

For loop 3:
-3000I3+3000I2-10-4000I3+5=0
3000I2-7000I3=-5


Putting this in matrix form and solving gives:
I1=-0.01A, I2=2.1mA, I3=1.923*10^-4A



Vout-R4*I3+V2=0
Vout=4000*1.923*10^-4 - 5
= -4.2308V

With the way Vout is drawn, it should be negative right?
 
  • #5
charlies1902 said:
...

With the way Vout is drawn, it should be negative right?
Yes, that's correct.

Notice that you didn't need to consider Loop 1 at all.
 
  • #6
rollingstein said:
To me simplest seems using the Superposition Theorem.

This was how I did it. Same answer.

wleJKO4.png
 
  • #7
If you recognize that R1 is "hidden" from the rest of the circuit by V1 (and so can be eliminated from the circuit entirely), and that V3 forms a supernode of Vout, you can write a single node equation and solve for Vout.

attachment.php?attachmentid=55198&stc=1&d=1359558784.gif
 

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  • #8
Thank you everyone!

The second part of the question asks what the power produced by each voltage source is.
This is easy with the equation P=IV.

The exact wording is "What's the power produced by each source."

Generally speaking, if a current enters the positive terminal of the voltage source that means the power is positive, right?

If a current enters the negative terminal of the voltage source that means the power is negative?

For V_1, the net current enters the negative terminal of V_1.
 
  • #9
If current exits the + terminal of a voltage source it is producing power (injecting energy into the circuit). If current enters the + terminal it is absorbing power (taking power out of the circuit). Whether you call the power positive or negative depends upon your point of view: are you adding up power being dissipated or power being generated?
 

1. What is current in a circuit?

Current is the flow of electric charge through a circuit. It is measured in amperes (A) and represents the rate at which electric charges (typically electrons) move through a conductor.

2. How is current related to voltage and resistance?

According to Ohm's Law, current is directly proportional to voltage and inversely proportional to resistance. This means that as voltage increases, current increases, and as resistance increases, current decreases.

3. How do you calculate current in a circuit?

Current can be calculated by dividing the voltage by the resistance, using the formula I = V/R. It can also be calculated by measuring the voltage across a circuit and the resistance of the circuit using a multimeter.

4. What is the difference between AC and DC current?

AC (alternating current) and DC (direct current) refer to the direction of current flow in a circuit. In AC, the direction of current changes periodically, while in DC, the current flows in one direction. Most household appliances use AC, while batteries and electronic devices use DC.

5. How does current affect the brightness of a light bulb?

The current in a circuit determines the brightness of a light bulb. As the current increases, the filament in the bulb heats up and emits more light. If the current is too high, it can cause the bulb to burn out. The resistance of the bulb also plays a role in determining the brightness, as higher resistance will decrease the current and therefore the brightness.

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