Kirchoff's Rules: Solve P28.19 Circuit

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In summary, the current flowing through the circuit is a (labeled a in the diagram), the voltage drops across the resistors are b+c, and according to Kirchoff's first law, a = b+c.
  • #1
clairez93
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Homework Statement


Determine the current in each branch of the circuit shown in Figure P28.19 (attached)


Homework Equations



Kirchoff's Rules:
[tex]\Sigma I_{in} = \Sigma I_{out}
[/tex]
[tex]\Sigma \Delta V = 0[/tex]



The Attempt at a Solution



I have no idea where to begin. It's in the Kirchoff's rules section, so I'm assuming those will be used, but how I don't know how to apply them.
 

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  • #2
Begin at the beginning. Explain what the KCL (1st equation) means, and what the KVL (2nd equation) means.

Then start with the KCL equations for the circuit. Call the bottom node ground, and write the 2 KCL equations for the two top nodes. There are three branches out of the top left node, and two branches out of the top right node... That gives you two equations and two unknowns (the top two node voltages are the unknowns)...

Show us some work, so that we can help you more. That's how it works here on the PF.
 
  • #3
Oh, and you might try following the "Similar Threads" links at the bottom of the page, in case that helps to get you started writing the equations here in your own thread.
 
  • #4
… give the unknowns names …

Hi clairez93! :smile:

Hint: start by calling the three unknown currents a b and c (with arrows).

Then write out all the Kirchoff's equations you can think of … what do you get? :smile:
 
  • #5
Okay, so I have this a current I labeled a going upward along the vertical line at the far right with the 1 ohm resistor in it. Then b and c going downwards along the lines with the 8 ohm resistor and the 5 and 1 ohm resistor line. (b for the 5 & 1 ohm resistor line, and c for the one with 8)

I'm thinking a = b+c according to Kirchoff's first?
 
  • #6
clairez93 said:
Okay, so I have this a current I labeled a going upward along the vertical line at the far right with the 1 ohm resistor in it. Then b and c going downwards along the lines with the 8 ohm resistor and the 5 and 1 ohm resistor line. (b for the 5 & 1 ohm resistor line, and c for the one with 8)

I'm thinking a = b+c according to Kirchoff's first?

Looks good! :smile:

Now what about the voltage drops across the resistors?

(going to bed now … :zzz:)
 

1. What are Kirchoff's Rules?

Kirchoff's Rules, also known as Kirchoff's Laws, are two fundamental principles in circuit analysis that are used to calculate the voltage and current in a circuit. These rules are based on the conservation of energy and charge.

2. What is P28.19 Circuit?

P28.19 Circuit refers to a specific circuit problem or diagram that is used to practice and apply Kirchoff's Rules. It is typically labeled as "P28.19" in textbooks or problem sets.

3. How do I solve a P28.19 Circuit using Kirchoff's Rules?

To solve a P28.19 Circuit, you first need to label the known values, such as resistances and voltage sources, and assign a direction to each current in the circuit. Then, you can apply Kirchoff's Rules, which state that the sum of the voltage drops in a closed loop is equal to the sum of the voltage sources, and the sum of the currents entering a junction is equal to the sum of the currents leaving the junction.

4. What are the limitations of Kirchoff's Rules?

Kirchoff's Rules assume ideal conditions in a circuit, such as no resistance in wires and ideal voltage sources. In real-life circuits, these assumptions may not hold true, leading to discrepancies between the predicted and actual values. Additionally, Kirchoff's Rules are only applicable to circuits with a single loop or multiple parallel loops.

5. Can I use Kirchoff's Rules to solve any circuit?

Kirchoff's Rules can be used to solve most circuits, but they may not be the most efficient method for complex circuits. In some cases, other techniques such as nodal analysis or mesh analysis may be more suitable. It is important to understand the limitations and applicability of each method when solving circuit problems.

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