Kirchhoff Circuit: Current, Resistors, Voltage

[kashmirekat]

Circuit Current

I have the circuit below (also attached as an image):
Note:
^^^^ & <<<< = resistors
[-]=power supply
...=just space
(-) & (+) indicates + & - side of battery
A,B represent the junctions

|-----^^^^------A-----^^^^------|
|......|......|
<......<......(-)
<......<......[-]
<......<......(+)
<......<......|
|......|......|
|----(+)[-](-)----B-----^^^^------|

R1=100 ohm (center far left)
R2=560 ohm (top left)
R3=330 ohm (center)
R4=300 ohm (top right)
R5=100 ohm (bottom right)
Va=1.5 V (bottom left)
Vb=1.6 V (center far right)
(This is also attached as an image. Sorry for the lack of quality, working quickly in paint.)

Okay, now that we've got the setup, I need help in determining my equations, well for the junction rule at least. My voltage equations are as follows:

Va-I1R1-I2R2-I3R3 = 0 (left loop)
Vb-I4R4-I3R3-I5R5 = 0 (right loop)
Va-I1R1-I2R2-I4R4+Vb-I5R5 = 0 (entire loop)

Okay, for the junction rules. I need two of them to have five equ for my five unknowns...which are the I.
Would they be,
I1+I2+I4=I3 (junction A)
I3=I5 (junction B)
Current in = Current out

Are these equations correct? I'm trying to find the current for each resistor and then go back and find the voltage. The latter is no problem, it's just determining that my equations are correct for current I.

Thank you for your assistance and have a nice day!
Christina

 

[kashmirekat]

Verify Equations

Please see attached image for circuit.

I have labeled all my current directions. For each Rn, that is the corresponding In. (ie. I1 goes w/R1)

I would like for you to verify my equations below for solving this circuit using Kirchhoff's Rules of voltage and current.

Junction Rules (Current In = Current out):
I2 = I3 + I4
I3 + I5 = I1 + I2 (OR) I3 + I5 = I ?

Voltage Rules ([delta]V=0):
Va-I1R1-I2R2-I3R3 = 0 (left loop)
Vb-I4R4-I3R3-I5R5 = 0 (right loop)
Va-I1R1-I2R2-I4R4+Vb-I5R5 = 0 (entire loop)

Thank you.

 

[Janitor]

I presume I3 is the current in the middle wire.

If so, doesn't I3+I5=I1? (Instead of "I3 + I5 = I1 + I2.")

 

[Janitor]

Your voltage equations look correct to me.

You can always eliminate some of the current variables by noting that I1=I2, etc.

 

[kashmirekat]

Would the equation be I3 + I5 = I (no subscript) or I3 + I5 = I1?

 

[Janitor]

If I1 is what one calls the current through R1, then I3 + I5 = I1.

 

[kashmirekat]

Ohhh, yeah. I knew that. :) Geez I am good at confusing myself.

Thank you for your help.

 

[jdavel]

kashmirekat,

Since I1 = I2 and I4 = I5, you really just have 3 different currents. Call them I12, I45 and I3. Then, the way you've defined directions, I12 = I3 + I45

Even as I'm writing this it looks like others are giving you the same help. Good luck!

 

[himanshu121]

Your making so many unnecessary unknowns

 

[jjiimmyy101]

I hope this explains your question.


This part got cut off

Ex) If you want to know the purple current, the equation is:

I1 - I2 = I

And since you already have I1 and I2 from earlier, I can be found easily.

I hope this helps :)