Solving for i and v_x: A Homework Challenge

In summary, the person is seeking help with finding the values of i and v_x in a circuit problem. They have attempted the problem in two different ways and are unsure of their answer. They are also questioning the accuracy of the provided solution and would appreciate any insights.
  • #1
SuperCat
26
1

Homework Statement


Find i and v_x
9f1bd6faa0ef539d5436d32024687883.png

Given answer:
d225a823c3560be5848ac8fba2392677.png
2. Homework Equations 3. The Attempt at a Solution
I have attempted the problem in two different manners, and I consistently reach a different answer. I would appreciate if someone would be willing to take the time to attempt the problem and confirm whether the provided solution is correct.

My answer:
i(t) = 5* e^(-5.6*t)
I have not attempted to solve for v_x yet, because I want to verify the first part of the answer.

Method 1: Apply KVL directly to the circuit
53ab3acec9b406125ac631548d64a84c.png


Method 2: Find the equivalent resistance at the inductor terminals with a test voltage source.
I am not showing the work for this method, but I did it this way as well and received the same answer as my first attempt.

If my attempt is wrong, I really would appreciate some insight into where I went wrong.
 
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  • #2
I think your result looks better than theirs! Considering that they used the unit V for both voltage and current in their answer, I suspect that they have an editing issue with the answer key.
 
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Likes SuperCat
  • #3
Good point, I completely managed to overlook that! I just couldn't find this listed in the errata for my book so I blindly trusted it.
 

1. What is the purpose of solving for i and v_x?

The purpose of solving for i and v_x is to determine the value of the unknown variables in a given equation or problem. Solving for i and v_x allows us to find the missing information needed to fully understand and solve the problem.

2. How do you solve for i and v_x?

To solve for i and v_x, you need to use algebraic principles and equations. Begin by isolating the i or v_x variable on one side of the equation, and then use inverse operations to solve for the variable. It may also be helpful to plug in known values for the other variables in the equation to simplify the process.

3. Can you solve for i and v_x in any type of equation?

Yes, you can solve for i and v_x in any type of equation, as long as there are enough known variables and the equation is solvable. However, the method for solving may vary depending on the type of equation.

4. What are some common mistakes when solving for i and v_x?

Some common mistakes when solving for i and v_x include forgetting to apply the distributive property, making errors when using inverse operations, and not checking the final answer for accuracy. It is important to carefully follow the steps of solving and double check your work to avoid these mistakes.

5. Are there any tips for solving for i and v_x efficiently?

Yes, there are a few tips for solving for i and v_x efficiently. First, make sure to carefully read and understand the problem before attempting to solve. It may also be helpful to use a calculator or graphing tool to check your work. Additionally, practicing with various types of equations can improve your speed and accuracy in solving for i and v_x.

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