# Why can we ignore certain circuit paths?

• xAly
In summary: R3 and/or R4 until it hit a higher potential (say Vr2h). At that point, the current would be forced to go back down the drawing to R2, completing the circuit. In summary, the current would keep flowing down R1 until it hit a higher potential and then would flow back up the other path.
xAly
Homework Statement
We have to determine the readings on the ammeter and voltmeter (see picture of circuit), given that ##\text{R}_1 = 4 \Omega, \text{R}_2 = 10 \Omega, \text{R}_3 = 7 \Omega, \text{R}_4 = 8 \Omega, \text{R}_5 = 6 \Omega, \text{R}_6 = 3 \Omega##
Relevant Equations
## \text{R} = \frac{\text{V}}{\text{I}} ##, Resistance in parallel and series.
I get really confused with these types of problems. I don't know how to break down the circuit properly. I tried to go anticlockwise and ignored the ammeter and the voltmeter as circuit components, which gave me R1 and R2 in series while R3 and R5 (in series) are in parallel with R4 and R6 (also in series). This gave me a final equivalent resistance of ##\frac{479}{24}##. But after checking my intermediate solution, it seems this approach is wrong. The solution starts with stating that we can ignore the lower half of the circuit and can only consider the resistors R1, R5 and R6 (so the problem becomes a lot easier). However I don't see why this is true and how one would spot this in similar problems.

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An (ideal) amperemeter is a perfect conductor. You can replace it by a wire in the circuit analysis.

mfb said:
An (ideal) amperemeter is a perfect conductor. You can replace it by a wire in the circuit analysis.

I still don't see how I can ignore the lower half of the circuit. Surely the current will still split up at the first junction?

xAly said:
I still don't see how I can ignore the lower half of the circuit. Surely the current will still split up at the first junction?
If the ammeter is treated as a perfect conductor then the potential at all three nodes to the left and right of the ammeter must be identical.

If the potential at all three nodes is identical then no current will flow through any resistors in the bottom half of the circuit. A circuit element through which no current flows might as well not be there. Remove it, leaving stub wires and an open circuit in its place. Then remove the stubs.

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This is the circuit with the amperemeter replaced by a wire and the voltmeter removed:

No current will flow through the lower resistors.

mfb said:
This is the circuit with the amperemeter replaced by a wire and the voltmeter removed:

View attachment 247589

No current will flow through the lower resistors.
Sorry, I am still quite not following. How does one justify the fact that there is no current? Jbriggs mentioned the fact that the potential must be the same at all the nodes, but isn't a wire also a perfect conductor and so there wouldn't be a current through the horizontal wire at all?

xAly said:
Sorry, I am still quite not following. How does one justify the fact that there is no current? Jbriggs mentioned the fact that the potential must be the same at all the nodes, but isn't a wire also a perfect conductor and so there wouldn't be a current through the horizontal wire at all?
Current flows through wires just fine. If there is any potential difference at all, an infinite current will flow. That is precisely why no potential difference can exist between two points on a wire.

xAly
The ammeter completely short-circuits the lower part. There is no potential difference across the ammeter because enough current flows through the ammeter at zero resistance to equalize the potential. Since there is no potential difference, there will be no (resisted) current flow on the lower path.
Mathematically, the fraction of current through path #1 in two parallel circuits is ## \frac {\frac {1}{R_1}}{\frac {1}{R_2} + \frac {1}{R_1}} = \frac {R_2}{R_1+R_2}##

(see Figure 1 of Current Divider)

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xAly
You can tell that there is no current flow in the lower half because if the voltage difference across a resistor (or a network of resistors) is zero then the current must also be zero. V = I*R. If the current through a resistor is zero, or the voltage across a resistor is zero (they are the same thing), then it doesn't matter what it's value is, so you can substitute whatever you want from 0 to ∞ without changing the solution to the problem. Yes, you are changing the circuit, but you are changing it to a circuit with exactly the same solution as the original one.

I found this to be an interesting discussion. I can not tell if the worry has been eliminated, so I would like to add my way of seeing that.

Current would be flowing down the schematic thru R1. Let the potential of the "horizontal wire" be Vh. What if some current tried to continue going down the drawing toward R2? That is a 10Ω resistor, so that current would be stymied -- unless the potential at the right end of R2 was lower than Vh. That is the only way positive charge has the attraction to the other end of a resistor. Well assume for now that it is lower there and call that Vr2r. Then what? That current would then have to go up R3 and/or R4. But that could only happen if the other end of R3 and R4 were lower than Vr2r. BUT, it is higher than Vr2r, because it is Vh! So that blows this whole "what if" story out of the water.

xAly

## 1. Why do we need to ignore certain circuit paths?

Ignoring certain circuit paths allows us to simplify complex circuits and focus on the most important parts. It also helps us save time and resources by not analyzing irrelevant paths.

## 2. How do we determine which circuit paths to ignore?

We can determine which circuit paths to ignore by using circuit analysis techniques such as Kirchhoff's laws and Ohm's law. These techniques help us identify the most significant paths in a circuit.

## 3. Can ignoring a circuit path affect the accuracy of our analysis?

Yes, ignoring a circuit path can affect the accuracy of our analysis if it is a significant part of the circuit. It is important to carefully consider which paths to ignore and ensure that they do not have a significant impact on the overall circuit behavior.

## 4. Are there any benefits to ignoring circuit paths?

Yes, there are benefits to ignoring certain circuit paths. It can help us simplify complex circuits, reduce the time and resources needed for analysis, and improve the overall efficiency of our circuit designs.

## 5. Can ignoring circuit paths lead to circuit failures?

In some cases, ignoring circuit paths can lead to circuit failures if the ignored path is critical to the circuit's functionality. It is important to carefully analyze and consider all paths before deciding which ones to ignore.

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