Kirchoff's loop rule with multiple voltage sources

In summary, the conversation discusses the issue of understanding the application of Kirchoff's loop rule in a circuit with multiple voltage sources. The main difficulty lies in remembering to use multiple equations to solve for multiple unknowns and understanding the relationship between the different voltage sources in the circuit. It is recommended to practice solving similar problems to improve understanding.
  • #1
Avatrin
245
6
Hi

Let's look at this:

img713.png


The issue I am having is that while I know that this is accurate:
img715.png


I just cannot wrap my head around why. I1 is a result of both voltage sources. So, while the equations clearly tell me that the voltage drop across the resistor R1 is I1R1, I cannot wrap my head around how this works in terms of Kirchoff's loop rule.
 
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  • #2
Doesn't I3 steal from I2 to make I1 different? Surely you accept that I3 is affected by E2.
 
  • #3
Yes, I get that part. It is the Kirchoff's loop rule that I cannot wrap my head around.

I1 is affected by both ε1 and ε2. Yet, I can use the equation above ignoring ε2. It is true regardless of ε2. That part I cannot wrap my head around.
 
  • #4
Ahhh i see.

I think it's not an electrical ambiguity, rather a temporary memory lapse in translating from the algebra you know well to the electricity that seems unfamiliar.

Back to algebra basics: It takes more than one equation to solve for more than one unknown.
So that one equation isn't the whole story.

We all stumble over these little difficulties. Work lots of homework problems..

old jim
 
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  • #5
If I understand correctly, your trouble seems to be the fact that the ε2 source is not represented in the first equation. The issue is that I2 is not a part of the loop equations in their most basic form. Rather I2 = I1 - I3, and there are only two equations that are necessary for the drawn circuit. Those loop equations need only use I1 & I3, so while ε2 is not directly reflected in the loop 1 equation, it is a part in as much as it factors into the 2nd loop equation as a boundary condition of I3's loop.

Follow Jim's advice and use the math and you will see that a change in ε2 does cause a change in the first equations value.
 

1. What is Kirchoff's loop rule with multiple voltage sources?

Kirchoff's loop rule, also known as Kirchoff's voltage law, states that the sum of all voltage drops in a closed loop circuit must equal the sum of all voltage sources in that same loop. When there are multiple voltage sources in a circuit, this rule helps to determine the direction and magnitude of the current flowing through the circuit.

2. How is Kirchoff's loop rule applied in a circuit with multiple voltage sources?

To apply Kirchoff's loop rule, you must first identify all the loops in the circuit. Then, for each loop, start at a point and follow the path, taking into account the direction of the current and the polarity of the voltage sources. As you go through each loop, add up all the voltage drops and set it equal to the sum of all the voltage sources in that loop. This will result in a set of equations that can be solved to determine the current flowing through each loop.

3. Can Kirchoff's loop rule be applied to circuits with only parallel elements?

Yes, Kirchoff's loop rule can be applied to circuits with only parallel elements. In this case, the voltage sources are connected in parallel, so the voltage drops across each source will be the same. This allows us to simplify the equations and solve for the current in each branch of the parallel circuit.

4. How does Kirchoff's loop rule account for the polarity of voltage sources?

Kirchoff's loop rule takes into account the polarity of voltage sources by considering the direction of the current flow. For example, if the current flows in the same direction as the polarity of a voltage source, the voltage drop will be positive. If the current flows in the opposite direction, the voltage drop will be negative. By incorporating the polarity of voltage sources, we can accurately determine the direction and magnitude of the current in a circuit with multiple voltage sources.

5. What are the limitations of Kirchoff's loop rule with multiple voltage sources?

Kirchoff's loop rule can become complicated and difficult to apply in circuits with a large number of voltage sources. Additionally, this rule does not take into account the internal resistance of voltage sources, which can affect the voltage drops in a circuit. In these cases, other methods, such as Thevenin's theorem, may be more useful in analyzing the circuit.

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