Problem:
Current Electricity: Kirchhoff's Laws (ully explained)
1. Finding Unknowns
Determine the unknowns in the circuit shown
2. How do electrical engineers use Kirchoff's current law and Kirchoff's voltage law to write a system of linear equations?
- Based on your explanation, write a system of linear equations for Problem 2 at the top of this page.
- Solve this system of linear equations for the unknowns.
- Do these answers contain important information about the circuit?
3. What are the main strengths of this method?
4. The main strengths of this method are:
(1) It can be used to make predictions.
(2) Since it is a linear model, it is easy to compute the dependent variable value.
(3) It has good effect when the dependent and independent variables show a good linear relation.
5. What are its main shortcomings?
Since it is a linear model, if the dependent and independent variables don't show a good linear relation, instead, a quadratic relationship, then it doesn't fit data well.
6. When would least squares be useful in the real world?
In the real world, when you need to make predictions for one variable Y based on one or more variables X, and if Y and X have a linear relation, then the least squares method would be useful.
7. Does the use of linear algebra make this method easier to understand or use?
Since when we use least squares method, we need to find a linear equation
Y=a+bx,
So, we need to determine the coefficients a and b so we have to solve for an equations system for a and b. Hence, the use of linear algebra make this method easier to understand or use.