Where Are the Hidden Loops in My Circuit?

[summersun]

I set this circuit up in my physics lab and measure all the required voltages, currents and resistors. I have been ask to prove that Kirchhoff's Voltage Rule is valid by applying it to all 7 loops. I am only able to find 3 loops and I am unsure as to where the other 4 are. I found 4 other possibilities however, they do not include the power supply and don't work according to Kirchhoff's Rule. Hopefully you can give me some hints as to where the other 4 loops are hiding

 

[tiny-tim]

I set this circuit up in my physics lab and measure all the required voltages, currents and resistors. I have been ask to prove that Kirchhoff's Voltage Rule is valid by applying it to all 7 loops. I am only able to find 3 loops and I am unsure as to where the other 4 are. I found 4 other possibilities however, they do not include the power supply and don't work according to Kirchhoff's Rule. Hopefully you can give me some hints as to where the other 4 loops are hiding

Hi summersun!

There are 3 "basic" loops.

Then there are another 3 loops each containing two "basic loops".

And there is 1 loop (the whole thing, obviously! ) containing all three "basic loops".

Total 7.

You can get 7 Kirchhoff's Rules equations, one for each loop, but only three of the equations will be independent (ie, you can work out any of the other 4 from any 3).

(The number of independent equations for any circuit is the same as the number of "basic loops".)

Try all the loops , and let us know if one isn't working.

 

[thomate1]

First of all, it is important to note that Kirchhoff's Voltage Rule (also known as Kirchhoff's Loop Rule) is a fundamental principle in circuit analysis and has been extensively tested and proven to be valid in numerous experiments. Therefore, it is important to approach this task with confidence and an open mind.

To address the issue of finding the other 4 loops, it is important to understand that loops in a circuit are formed by a continuous path of conductors and components. Therefore, it is possible that the loops may be hidden within the circuit components or may not be immediately obvious. Some possible reasons for not being able to find the other 4 loops could be:

1. The loops may be formed by components that are not physically connected but are electrically connected, such as capacitors or inductors. In such cases, the loops may not be visually apparent but can be identified by tracing the flow of current through the circuit.

2. The loops may be formed by virtual connections, such as a voltage source connected to a ground point. These loops may not be immediately visible but can be identified by considering the voltage drops and gains around the circuit.

3. The power supply itself may be considered as a loop, as it is connected to the circuit and provides a voltage source. This loop should be included in the analysis.

4. It is also possible that some of the loops may be redundant and can be eliminated from the analysis without affecting the validity of Kirchhoff's Voltage Rule. This can be determined by carefully analyzing the circuit and identifying any parallel or series connections.

Therefore, my suggestion would be to carefully review the circuit and the components to identify any possible hidden or virtual connections. Additionally, it may be helpful to redraw the circuit in a different configuration to better visualize the loops. I would also recommend consulting with your lab instructor or a fellow student for a fresh perspective and potential hints on where the other 4 loops may be hiding.

In conclusion, Kirchhoff's Voltage Rule is a well-established principle in circuit analysis and has been proven to be valid in numerous experiments. While it may be challenging to identify all 7 loops in a circuit, with careful analysis and an open mind, it is possible to find and apply Kirchhoff's Rule to all loops.