Kirchhoff's Laws: Homework Solutions Check

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In summary, The conversation is about identifying possible mistakes in equations related to electrical circuits. The equations discussed are \sum I_{in} = \sum I_{out}, \sum \epsilon = \sum pd, I = I_1 + I_2, and 12=4I_1 +3I, with the main focus on the signs of I1 and I2. The conversation also touches on the use of + signs with current arrows and their possible redundancy. The conclusion is that all currents should be taken as positive for the given directions.
  • #1
frazdaz
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Homework Statement



2s1n338.png


Homework Equations



[tex]\sum I_{in} = \sum I_{out}[/tex]
[tex]\sum \epsilon = \sum pd[/tex]

The Attempt at a Solution



Can anyone identify any mistakes in these? Probably signs

[tex]I = I_1 + I_2[/tex]
[tex]12=4I_1 +3I[/tex]
[tex]5=4I_1 - 2I_2[/tex]
[tex]12-5=2I_2+3I[/tex]
 
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  • #2
What let's you think there are any mistakes ?
 
  • #3
BvU said:
What let's you think there are any mistakes ?
The answers have I1 and I2 with opposite signs. I get them both as positive.
 
  • #4
I make all currents positive for the directions shown.

I'm not sure what is achieved by that + sign accompanying each current arrow? It seems superfluous if it duplicates the function of the arrowhead, and just clutters the diagram.
 
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  • #5
NascentOxygen said:
I make all currents positive for the directions shown.

I'm not sure what is achieved by that + sign accompanying each current arrow? It seems superfluous if it duplicates the function of the arrowhead, and just clutters the diagram.
Well that's good news. And, yeah, I guess it's just intended to help with the maths side of things.
 

FAQ: Kirchhoff's Laws: Homework Solutions Check

What are Kirchhoff's Laws?

Kirchhoff's Laws are a set of fundamental principles in electrical circuit analysis. They were developed by German physicist Gustav Kirchhoff in the mid-19th century and are used to describe the behavior of electric currents and voltages in circuits.

What is the first law of Kirchhoff?

The first law, also known as Kirchhoff's Current Law (KCL), states that the algebraic sum of currents entering and leaving a node (or junction) in a circuit must equal zero. This law is based on the principle of conservation of charge.

What is the second law of Kirchhoff?

The second law, also known as Kirchhoff's Voltage Law (KVL), states that the algebraic sum of voltages around a closed loop in a circuit must equal zero. This law is based on the principle of conservation of energy.

How do I apply Kirchhoff's Laws to solve circuit problems?

To use Kirchhoff's Laws in circuit analysis, one must first draw a circuit diagram and label all the elements. Then, use KCL to analyze the currents at each node and KVL to analyze the voltages around each loop. Finally, use simultaneous equations to solve for the unknown values.

What are some common mistakes when applying Kirchhoff's Laws?

Some common mistakes include not properly identifying the nodes and loops in a circuit, forgetting to include all the elements in the circuit, and not correctly assigning the direction of currents and voltages. It's also important to double-check the signs and algebra when solving the simultaneous equations.

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