3A. Consider the circuit shown below: a.) Carefully draw or cut and tape a copy

Question

3A. Consider the circuit shown below:  

a.) Carefully draw or cut and tape a copy of the circuit in your bluebook. Be sure to make a large drawing so that you will have room to add additional information to the drawing!  

b.) Draw and label arrows showing the assumed (or guessed) directions of the currents Ia, Ib , and Ic in branches a, b, and c. Note – branches are NOT loops!, and you should take care to NOT draw your branch currents as loops! Keep the branch currents you draw entirely confined to the branches in which they are flowing!    

c.) Place “+” and “-” signs (polarity signs) on the ends of the resistors that correspond to the current directions you assigned in step b.  

d.) Apply Kirchoff’s Voltage Law to the left hand loop. In doing so, clearly label the starting point for the loop, and the direction of travel around the loop. Then write the initial form of the KVL equation showing the changes in potential (“voltages”) in the order in which they occur as you traverse the loop. Write a second version of the KVL equation with the terms rearranged in “standard form”. Finally, write a final version of the KVL equation with the known numerical values (of the resistors and Emfs) substituted in.  

e.) Apply Kirchoff’s Voltage Law to the outer (periphery) loop. In doing so, clearly label the starting point for the loop, and the direction of travel around the loop. Then write the initial form of the KVL equation showing the changes in potential (“voltages”) in the order in which they occur as you traverse the loop. Write a second version of the KVL equation with the terms rearranged in “standard form”. Finally, write a final version of the KVL equation with the known numerical values (of the resistors and Emfs) substituted in. Apply Kirchoff’s Current Law to either node A or node B of the circuit. In doing so, clearly indicate the node you have decided to use. Then write the KCL equation in standard form.  

f.) Use your results from steps d, e, and f above to write the “augmented matrix” that would need to be “solved” (put in “row reduced echelon form”) to find the unknown currents.  

At this point you are done with problem 3A! You do not have to actually solve the system and find the unknown currents (which is just tedious algebra for those of you who do not have or know how to use a calculator with matrix capabilities)! Of course, you might want to solve the system to increase your confidence in your earlier work, but this is not necessary and I do not need (or even want) to see that work.  

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Explanation / Answer

Where is circuit? We need circuit to explain kvl and kcl statement s with in detail.

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