Deriving current expression from the info given

In summary, the conversation is about a question regarding equation 4.1.11 on page 67 of a research paper. The person is confused about how the equation is derived and is asking for clarification. The response provides an explanation, stating that the equation was not derived from the mentioned equations and instead came from 4.1.8 and 4.1.9. It also explains how 4.1.11 factors out a term and replaces two terms with one.
  • #1
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Homework Statement



I am doing some research and reading this: http://www.csuohio.edu/ece/theses/2004/Bhavin.pdf

I don't understand how the equation 4.1.11 on page 67 is derived.
Can anyone help clarify?


Homework Equations


(As in the pdf file)


The Attempt at a Solution


I have tried to understand it, but couldnt.
 
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  • #2
It might be because this expression was not derived from the equations mentioned; in fact there IS no 4.2.3 at all, and 4.2.2 has nothing to do with 4.1.11. It appears this came from 4.1.8 and 4.1.9, where the expression for T(s) is substituted into 4.1.8 which is then solved for I(s). 4.1.11 factors out the omega(s) term and replaces the two j terms with one J term.
 

1. What is the process for deriving a current expression from the information given?

The process for deriving a current expression involves analyzing the given information, identifying relevant equations or principles, and manipulating them to solve for the current. This may include using Ohm's Law, Kirchhoff's Laws, or other circuit analysis techniques.

2. How do you determine which equations to use when deriving a current expression?

The equations used for deriving a current expression will depend on the specific circuit or system being analyzed. Generally, Ohm's Law is used for simple resistive circuits, while Kirchhoff's Laws are used for more complex circuits with multiple components and branches.

3. Can you provide an example of deriving a current expression?

Sure! Let's say we have a simple circuit with a 12V battery and a 4 ohm resistor. To derive the current expression, we would use Ohm's Law (I = V/R) and plug in the values: I = 12V/4ohm = 3A. So, the current in the circuit is 3 amps.

4. What factors can affect the accuracy of a derived current expression?

The accuracy of a derived current expression can be affected by a number of factors, including the precision of the given values, the assumptions made in the analysis, and any external factors that may impact the circuit (such as temperature or interference).

5. Are there any common mistakes to watch out for when deriving a current expression?

Yes, there are a few common mistakes that can occur when deriving a current expression. These include using incorrect units, forgetting to account for the direction of current flow, and overlooking parallel or series connections between components. It's important to double check your work and ensure all equations and principles are being applied correctly.

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