# Find Vo in the circuit / current direction / potential direction

• Engineering
• Color_of_Cyan
In summary: Sorry.In summary, the given circuit has a potential drop of 8V across the 4Ω resistor and an unknown voltage, Vo, in the circuit. Using the equations V = IR, KVL, and KCL, the circuit can be simplified to show that the current in the right branch is 2A, and consequently, the current in the 8Ω resistor is also 2A. This results in a potential difference of 16V across the 8Ω resistor. In the left branch, the resistors can be simplified to 4Ω and the potential difference is also found to be 24V. However, without being given the direction of the potential drop Va, it is impossible to determine
Color_of_Cyan

## Homework Statement

http://imageshack.us/a/img29/9056/homeworkprob10.jpg

Given: Va = 8V. Find Vo in the circuit.

## Homework Equations

V = IR,

KVL, KCL

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

Current division (only for two resistors in parallel):
(current through parallel resistor) = [ (OTHER resistance)/(sum of resistors) ](total incoming current)

## The Attempt at a Solution

I think you can redraw it like this:

http://img24.imageshack.us/img24/8245/homeworkprob10redraw.jpg

And since 8V = Va across the 4Ω resistor, V = IR means the current in the whole right node means that I = V/R, and then I = 8V / 4Ω

I = 2A in the right branch right?

Then I = 2A also in the 8Ω resistor in series with it,

so then V = IR for the 8Ω resistor means, V = (2A)(8Ω), V = 16V over the 8Ω resistor

Adding these, V = 24V for the entire right branch.

Left branch resistors is simplified to 4Ω and then you can say V = 24V for it because of being in parallel, right?

Then I = 6A for the left because I = V/R --> 24V/4Ω

then that means 8A is supplied from the middle to both,

but then that means V = (3Ω)(8A) means V = 24V through the middle 3Ω resistor

It can't be more than 24V because it's in parallel right? There was no direction given for Va in the first place and that's confusing. The answer for Vo is given so the only thing that would make sense is if V = -24V for the middle 3Ω resistor and then Vo = 48V (which is also the answer, and just thought of this now).

Is there a better way to tell if either the current or potential in the middle branch is + or - then given only Va first? Again, I just figured it out for the middle branch just now but it's still kind of confusing so, thanks anyway.

Last edited by a moderator:
Without being given the direction of the potential drop Va, you can't tell which direction the current is flowing. So there will be two possible answers, on for each choice of direction of Va.

Remember that if the central resistor is dropping a certain amount of potential, the voltage source Vo will have to make up the difference so that their sum matches the required branch voltages.

Cyan..

Your approach isn't correct. The 2A doesn't flow through the 8 Ohms. I redrew it like this...

PS Vo is on the right.

#### Attachments

• redrawn.png
2.6 KB · Views: 641
PPS: Two of the resistors don't effect Vo.

CWatters said:
Cyan..

Your approach isn't correct. The 2A doesn't flow through the 8 Ohms. I redrew it like this...

PS Vo is on the right.

Hmm. The way I interpret the problem Va is not a voltage source, it's the potential drop across the 4Ω resistor due to the current flowing though it. The only independent voltage source in the circuit is Vo.

Color_of_Cyan said:

## Homework Statement

Is there a better way to tell if either the current or potential in the middle branch is + or - then given only Va first? Again, I just figured it out for the middle branch just now but it's still kind of confusing so, thanks anyway.

If you're given a potential drop without its direction being specified, then all you can do is look at the circuit and make deductions/assumptions. Like, looking at the indicated polarity of Vo, if it is assumed that Vo is a positive value then the current can only flow one way through it since it's the only source in the circuit. That in turn tells you which way the current must flow in the branches, hence the polarity of Va.

When these situations crop up on assignments or exams, be sure to explicitly state your assumptions along with your solution.

gneill said:
If you're given a potential drop without its direction being specified, then all you can do is look at the circuit and make deductions/assumptions. Like, looking at the indicated polarity of Vo, if it is assumed that Vo is a positive value then the current can only flow one way through it since it's the only source in the circuit. That in turn tells you which way the current must flow in the branches, hence the polarity of Va.

When these situations crop up on assignments or exams, be sure to explicitly state your assumptions along with your solution.

Okay, thanks. And yes, Va was the potential drop across that resistor, and neither the drop direction or current direction were given. It's just given from being positive and then the direction of Vo.

gneill said:
Hmm. The way I interpret the problem Va is not a voltage source, it's the potential drop across the 4Ω resistor due to the current flowing though it. The only independent voltage source in the circuit is Vo.

Insert red face.

That makes much more sense now I look at it again. I was fooled by the subscript on Vo.

## 1. How do you find Vo in a circuit?

To find Vo (output voltage) in a circuit, you can use Kirchhoff's voltage law (KVL) or Ohm's law. KVL states that the sum of all voltage drops around a closed loop in a circuit is equal to the sum of all voltage sources. Ohm's law states that voltage (V) is equal to current (I) multiplied by resistance (R). By using these principles and analyzing the circuit, you can determine the value of Vo.

## 2. How do you determine the current direction in a circuit?

To determine the current direction in a circuit, you can use the passive sign convention. According to this convention, current flows from positive to negative terminals of a voltage source and from higher to lower potential. You can also use Kirchhoff's current law (KCL), which states that the sum of all currents entering a node in a circuit is equal to the sum of all currents leaving that node.

## 3. How can you identify the potential direction in a circuit?

To identify the potential direction in a circuit, you can use the concept of voltage polarity. The positive terminal of a voltage source has a higher potential than the negative terminal. By tracing the direction of current flow and keeping track of voltage polarities, you can determine the potential direction in a circuit.

## 4. What factors can affect the accuracy of finding Vo in a circuit?

The accuracy of finding Vo in a circuit can be affected by several factors, such as circuit complexity, component tolerances, and measurement errors. Additionally, any circuit elements that are not ideal, such as resistors with non-linear characteristics, can also impact the accuracy of the result.

## 5. Can you determine Vo without using mathematical equations?

In some cases, it is possible to determine Vo without using mathematical equations. For example, if the circuit is purely resistive, you can use a voltage divider circuit to find the output voltage. You can also use graphical analysis techniques such as the load line method to find Vo. However, for more complex circuits, mathematical equations are necessary to accurately determine Vo.

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