Science:Math Exam Resources/Courses/MATH152/April 2022/Question B5 (b)
• QA01 • QA02 • QA03 • QA04 • QA05 • QA06 • QA07 • QA08 • QA09 • QA10 • QA11 • QA12 • QA13 • QA14 • QA15 • QA16 • QA17 • QA18 • QA19 • QA20 • QB1 (a) • QB1 (b) • QB2 (a) • QB2 (b) • QB2 (c) • QB3 (a) • QB3 (b) • QB4 (a) • QB4 (b) • QB4 (c) • QB5 (a) • QB5 (b) • QB5 (c) •
Question B5 (b) 

In the right circuit the differential equations are Find the second differential equation . The equation should only involve . 
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! 
Hint 

Kirchoff’s current law states that the sum of the currents entering a junction must equal the sum of the currents exiting a junction. Can you use this and Kirchoff’s voltage law to write in terms of , , and ? 
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.

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. We are given in the question statement, so what remains is to write in terms of , , and . First use Kirchoff’s current law on the upper middle junction: . Rearranging gives . Now, to determine , we use Kirchoff’s voltage law on the left loop: . Rearranging this and substituting it back into the equation for gives . Thus, the second differential equation is 