Science:Math Exam Resources/Courses/MATH152/April 2016/Question A 26
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Question A 26 

Questions A25 and A26 concern the circuits above. In the left diagram, is the current through the current source and is the voltage across it, to be determined. A26: The left circuit above has solution
with all currents in Amps and potentials in Volts. Use this information to derive a differential equation system for , , and in the right hand circuit where the two capacitors are 2 Farads and the inductor is 0.1 Henry. 
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! 
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Hint 

Recall that capacitor equation states that
where the voltage across the capacitor is , the capacitance is , and that the constructive equation for inductors states
where is the inductance of the inductor. Take careful notice of the direction of the currents and . One of these currents is pointing in the direction of the voltage across the capacitor and the other is pointing in the opposite direction. 
Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

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Solution 

Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies. Following the hint, we have
Answer: <math> \color{blue} \begin{bmatrix} \frac{d V_1}{dt} \\ \frac{dV_2}{dt} \\ \frac{dI}{dt} \end{bmatrix} = \begin{bmatrix} 1/3 & 1/6 & 1/6 \\ 1/6 & 1/6 & 1/6 \\ 110/3 & 20/3 & 10/3 \end{bmatrix} \begin{bmatrix} I \\ V_1 \\ V_2 \end{bmatrix} 
Please rate how easy you found this problem:
Hard Easy 
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