Electricity Circuit Analysis: Finding Voltage, Current, and Resistance Values

[Genesis]

Hi, I have made a thread about electricity a couple of days ago, which Jimmy kindly helped me out with, but I am again, stuck on the last question (most dificult question).

Here is the diagram that I have scanned: http://gallery.cybertarp.com/albums/userpics/12541/electricity2.gif

Basically, I need to find voltage drop across the resistor (V), current flowing through the resistor (I), the resistance constant (R) mainly using this equation: V = IR

I need to find: R1, R2, R3, R4, Rt (total), I1, I2, I3, I4, It (total), V1, V2, V3, V4 and Vt (total).

Well, when I tried to solve this question, I thought because I1 = 8.5A and it is in series with the power source, It = 8.5A also. Then I got stuck. I though I4 is also equal to 8.5A, but apparently, the answer says it's not.

It's quite surprising to see that V2 and V3 have different values. I thought since they are in parallel relationship, they must be the same.

Here are the answers for your convinience:
It = 8.5A
Rt = 4.47ohms
Vt = 38V
I1 = 8.5A
R1 = 2ohms
V1 = 17V
I2 = 3A
R2 = 7ohms
V2 = 21V
I3 = 5.5A
R3 = 2.32ohms
V3 = 12.75V
I4 = 5.5A
R4 = 1.5ohms
V4 = 8.25V

Thank you very much for your help!

 

[Jimmy]

Hello Genesis,

This circuit is a bit tricky.

The first thing I did was edit your image. It is the same circuit electrically but I shifted the position of R4 around to make it simpler to understand.

http://members.aol.com/jrzycrim01/electricity3.gif

The first thing you can find is Rt. Since the total current is flowing through R1 and we know the total voltage, Rt=Et/IR1.

Rt=4.47 ohms; Et=38 V; It=8.5 A

Now let's look at R3 and R4. R3 and R4 are in series with each other and are parallel with R2. Since R3 and R4 are in series, the same current flows through both. We know that IR3 is 5.5A and IR4 is also 5.5A. Knowing that, we can find ER4 since it's resistance is given. ER4=5.5A * 1.5 ohms which is 8.25 V.

Now since R3 and R4 are parallel with R2, the voltages across both R3 and R4 are equal to the voltage across R2. We know ER4=8.25 volts, so ER3=ER2-ER4 which is 12.75 V.

Now we know ER3 and IR3 so R3 = ER3/IR3 = 2.32 ohms.

Next we can calculate IR2. We know the total current is 8.5A. We know the current through the R3R4 branch is 5.5A. Knowing that the current divides between parallel branches, we can subtract the current through R3R4 from the total to give us the current through the remaining branch. IR2=It-IR3R4=3A.

Knowing ER2 and IR2 we can find R2. 21V/3A=7 ohms.

The voltage across R1 is simply the total voltage minus the voltage which is dropped across the parallel branches. 21V is dropped across R2 and R3R4. Since R1 is in series with the rest of the circuit, the voltage will divide between R1 and the R2,R3R4 branches. ER1=38V-21V=17V. Finally, we can find R1. R1=ER1/IR1=2 ohms.

Remember, current will stay the same through components in series but divide through parallel branches. Voltages will be equal across parallel branches but will divide across components in series.

R2 and R3 aren't at the same voltage potential because R4 is in series with R3 and that 21 volts is divided across R3 and R4.

It helps to redraw the circuit when it's confusing. Look at my diagram and compare it to yours. You can figure out that it is the same electrically because the components are at the same potential. I just moved R4 around. You might think you could do the same with R1; that is move R1 in series with R2, but if you look at the diagram, it would not be the same circuit electrically.


When I was in tech school, I found it helpful to trace the current paths in complex circuits like this. You can see right away where the current splits and where the current is the same through components in series. Refer to this image:

http://members.aol.com/jrzycrim01/electricity4.gif

You can see that the current splits at the junction of R2 and R4 but the same current is flowing through R4 and R3.

Pardon my use of the Symbol E for voltage. That's how I was taught and I've used it so much I can't stop! I think V is used by electricians but I can't be sure about that. I'll have to look it up.

Hope this helps and good luck.

 

[Genesis]

Wow... I don't know what to say! THANKS SO MUCH! I think I got the answers. Thanks again!