Science:Math Exam Resources/Courses/MATH152/April 2022/Question B5 (a)
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Question B5 (a) 

This problem concerns the two circuits below. The voltage drops are the currents are . The capacitances are and the inductance is (a) In the left circuit assume that and are some given numbers. Use the loop current method to solve for in terms of 
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 hints below. Read the first one and consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! If after a while you are still stuck, go for the next hint. 
Hint 1 

The loop currents for this problem, and , are already assigned to loops. Recall that if a current source exists in a loop, the loop current must equal the current source. 
Hint 2 

You will have to use Kirchoff’s voltage law, which says that the sum of voltage changes in a loop must equal zero. Note that that in order to use this with the given circuits, you will also need Ohm’s law: if a current flows through a resistance , then the voltage drop across the resistance is . 
Checking a solution serves two purposes: helping you if, after having used all the hints, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. We are given the two loops to which the currents and correspond, and we can use Kirchoff’s voltage law on these loops to determine equations for , , and . In the left loop: In the right loop: And, we also know that if there is a current source in a loop, the loop current must equal the current source, so we have . Rearranging gives us 