Finding Current and Voltage through R2

[ckboii89]

Homework Statement

This was a test question. I know how to solve it. I just need someone to explain to me how to derive current for each side of the battery. I did it wrong on the test and failed miserably. But hey, i caught my mistake while thinking about it after. *note, the actual test did not include variables, i just threw them in there to simulate to get a better understanding. The test was asked to derive the current and voltage across R2

Homework Equations

Super Position, KCL, Ohms law

The Attempt at a Solution

Do Superposition on each battery. Find the current coming of the batteries by simplifying circuit. Then current going through R2 is the sum of the currents from the 2 batteries. Then use Ohms law to find voltage across resistor. HOWEVER, i noticed that from the simulating, the current through 1 battery is half of the total current through R2! I made a huge mistake during the test, and derived that the current from 1 battery is the amount through R2! Can someone explain where intuitively to derive a 1/2 number for the current from superposition?

 

[jafferrox]

you can either use kcl or superposition, KCL is easier to use.
label the node A
let the current from the left battery be I1 flow to node A, the current from the right battery I2 flow to node A and current going to the middle resistor I3
KCL At node A: I3 = I1+I2
replace currents with ohms law: (VA/100) = (1-VA/100) + (1-VA/100)
multiply both sides by 100: VA = 1-VA + 1-VA
VA = 2 -2VA
3VA = 2
VA = 2/3 V (which is the voltage across resitor R2

 

[gneill]

Do Superposition on each battery. Find the current coming of the batteries by simplifying circuit. Then current going through R2 is the sum of the currents from the 2 batteries. Then use Ohms law to find voltage across resistor. HOWEVER, i noticed that from the simulating, the current through 1 battery is half of the total current through R2! I made a huge mistake during the test, and derived that the current from 1 battery is the amount through R2! Can someone explain where intuitively to derive a 1/2 number for the current from superposition?

Just look at the symmetry of the circuit: Identical battery voltages with identical series resistances feeding the central node. There is no way to distinguish one from the other. Therefore they must produce the same currents.

 

[ckboii89]

actually, right before i went to sleep, i realized i did this question right. I assumed my methodology was wrong( i didnt get my exam back yet). What i did during the exam to find the current was after finding the total current from 1 battery, I used current division and found the current from going into R3. That itself would have given me the 1/2 i needed. Now, what i did after was say that the total current from through R3 is the combination of the 2 currents going into the node. Is this ok to say this? Also, i said the total voltage drop is the combination of the voltage drop between for R3 from each superposition case. The test specifically asked to do in Superposition

 

[gneill]

actually, right before i went to sleep, i realized i did this question right. I assumed my methodology was wrong( i didnt get my exam back yet). What i did during the exam to find the current was after finding the total current from 1 battery, I used current division and found the current from going into R3. That itself would have given me the 1/2 i needed. Now, what i did after was say that the total current from through R3 is the combination of the 2 currents going into the node. Is this ok to say this? Also, i said the total voltage drop is the combination of the voltage drop between for R3 from each superposition case. The test specifically asked to do in Superposition

Not sure I follow your "from going into" and "from through" phrases. But I'd have thought you'd suppress one source and find the resulting current through and voltage across R2. Then invoking symmetry, double the values to account for the other source.

 

[ckboii89]

Not sure I follow your "from going into" and "from through" phrases. But I'd have thought you'd suppress one source and find the resulting current through and voltage across R2. Then invoking symmetry, double the values to account for the other source.

From following your reply, I think i basically did what you said. Found the current and voltage across R2 for each case, and then add them up in the end to say that the voltage and current is a combination of both superposition cases. Is this correct to do? If it is, I will have to argue with my grader or whoever to redeem points on my test

 

[gneill]

From following your reply, I think i basically did what you said. Found the current and voltage across R2 for each case, and then add them up in the end to say that the voltage and current is a combination of both superposition cases. Is this correct to do? If it is, I will have to argue with my grader or whoever to redeem points on my test

Yes, that's the essential gist of superposition. The net result is the linear sum due to the individual stimuli.