How Do You Solve Complex Kirchhoff's Law Problems?

In summary, the student attempted to solve equations for current through a series of resistors, but was unsuccessful because of an error in one of the equations.
  • #1
BirdK
3
0

Homework Statement


http://file:///Users/jarrettwingfield1/Desktop/Screen%20Shot%202016-09-29%20at%205.29.21%20PM.png My professor told me my equations were correct, but I do not know how to find the current through each resistor mathematically, and every example I find online is too simple so it doesn't help me.
My equations are: i1=i2+i3; -2i2 - 6i1 = -8 ; 2i2- 4i3 = -12
An online calculator says i1=0.857 i2=-1.429 and i3= 2.286

Homework Equations

The Attempt at a Solution

question 4a.jpg
Screen Shot 2016-09-29 at 5.29.21 PM.png

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question 4.jpg
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  • #2
Hi BirdK, Welcome to Physics Forums.

Your image is not visible, likely because it's hosted on your machine. Can you upload it? (Use the UPLOAD icon at the bottom right of the reply edit window).

You need to show some details of your attempt.
 
  • #3
Well I can't seem to figure out the upload thing, maybe because its a mac. But I am certain that my equations are set up correctly, so if someone can just show me how to do the math. I've attempted it several times, but my professor hasn't showed us how to do all the different types of these equations.
 
  • #4
If the image is in a file on your computer then the UPLOAD mechanism should be able to open a file list via your machine's operating system for selection. If not then perhaps the mechanism is blocked on your machine (security issue?). Otherwise, you should be able to cut and paste a "snipped" screen grab. Failing that, upload your image to a hosting side and paste a URL.

Regarding your equations, helpers won't do the math for you or show you step by step. You need to show what you've attempted in detail and they will point out errors, make suggestions, give hints and so on.
 
  • #5
I attached the problem and my work. Where it says 3(4), that just means I multiplied equation 3 by 4, to add to the equation of 1+2
 
  • #6
I'm having difficulty interpreting your handwritten work, but I can see that the results you're getting are not correct.

I've spotted one error in the first block of equations where you summed ##-6 I_3## and ##-16 I_3## and arrived at ##-24 I_3##, which is not right. I gave up after that.

You should endeavor to make the math you present more clear for others to read, preferably with some commentary to describe what you're doing at each step. Ideally you'd type in your equations so that they can be quoted in replies. LaTeX is a wonderful thing :smile:
 

FAQ: How Do You Solve Complex Kirchhoff's Law Problems?

What is Kirchoff's Law?

Kirchoff's Law, also known as Kirchoff's circuit laws, refers to two fundamental principles in electrical engineering that describe the behavior of electric circuits. The first law, known as Kirchoff's Current Law, states that the sum of currents entering a node (or junction) in a circuit must equal the sum of currents leaving the node. The second law, known as Kirchoff's Voltage Law, states that the sum of voltage drops around a closed loop in a circuit must equal the sum of voltage sources in that loop.

Why is it important to understand Kirchoff's Law?

Kirchoff's Law is crucial in understanding and analyzing complex electrical circuits. It allows us to determine the current and voltage values at different points in a circuit, which is essential in designing and troubleshooting electronic systems. Without a solid understanding of Kirchoff's Law, it would be challenging to comprehend and work with circuits, especially in advanced applications such as power systems and telecommunications.

How do you apply Kirchoff's Law in a circuit?

To apply Kirchoff's Law, you need to follow two steps: first, identify all the nodes and branches in the circuit. A node is a point in the circuit where two or more branches meet, while a branch is a path between two nodes. Then, write down Kirchoff's Current Law and Kirchoff's Voltage Law equations for each node and loop, respectively. Finally, solve the resulting equations simultaneously to determine the unknown values.

What are some common mistakes when using Kirchoff's Law?

One common mistake when using Kirchoff's Law is forgetting to account for the direction of the currents and voltages in the circuit. It is crucial to follow the convention of positive and negative signs to ensure the accuracy of the results. Another mistake is not considering the voltage drop across resistors or other components in the circuit, which can affect the overall calculations.

Can Kirchoff's Law be applied to any circuit?

Yes, Kirchoff's Law can be applied to any circuit, whether it is a simple series or parallel circuit or a more complex network of interconnected components. However, it is essential to note that Kirchoff's Law is based on certain assumptions, such as ideal components and steady-state conditions, and may not be accurate in all situations. In such cases, more advanced techniques, such as nodal analysis or mesh analysis, may be necessary.

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