Brute-force Equations
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1) Part 1: Brute Force
To start, set up a set of 8 linearly-independent equations that can be used to solve for all branch voltages and currents in the circuit below using the brute-force method discussed in lecture/recitation this week. Recall that the brute-force method involves the following steps:
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Define a voltage and current variable for each branch, following the convention that the current variable should always defined as flowing into the terminal labeled as + in the voltage variable.
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In terms of those variables, write:
- One constitutive equation for each branch
- One KCL equation for each node in the circuit except 1
- Enough linearly-independent KVL equations to give you the necessary number of equations to solve for all of the variables in the circuit
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Solve those equations.
Clearly label all variables directly on the circuit diagram (including its direction), and for each equation, indicate whether it originates from KCL, KVL, or the constitutive relations of the elements. To start, be pedantic and write out all of the equations in terms of your variables without simplifying anything or substituting values in.
Then, solve the circuit, finding the current through and voltage across every element. You are welcome to do this step by hand, or to use a computer (for example, you might use Wolfram Alpha or SymPy to solve symbolically, or convert to matrix form and use NumPy).
A complete answer to this question will include both a complete set of brute-force equations (labeled as described above) and a solution with units labeled.
2) Part 2: Node Method
Next, use the node method to solve the circuit, showing all of your work (and clearly indicating which node you chose as your reference point). This should involve solving a single equation with a single unknown value. Finally, verify and show that your answers are consistent with those from part 1.
Upload your answer as a PDF file below. Your most recent submission before the problem deadline is the one that will be graded. Please do not include any identifying information in your submission so that we can grade your work anonymously.
