Solving an Electricity Question: Circuit Analysis for V, I, and R Values"

[Genesis]

Hi, I need help with an electricity question where it requires for me to see the circuit diagram and figure out: volage drop across the resistor (V), current flowing through the resistor (I), the resistance constant (R).

Here is the link to the diagram that I've scanned:
http://gallery.cybertarp.com/albums/userpics/12541/electricity.gif

Basically, I need to figure out all the V, I and R for each resistor,

so basically I need to figure out everything, which are...

R1, R2, R3, Rt (total), I1, I2, I3, It (total), V1, V2, V3 and Vt (total)

I thought I could find Rt by using the equation:

Rt = R1 + R2 + R3 or 1/Rt = 1/R1 + 1/R2 + 1/R3, but none of those work. I think the only way to start this question is to figure out Rt first.

By the way, the answers are:

It = 12A
Rt = 11 ohms
Vt = 132V
I1 = 12A
R1 = 7.67 ohms
V1 = 92V
I2 = 4A
R2 = 10 ohms
V2 = 40V
I3 = 8A
R3 = 5 ohms
V3 = 40V

I greatly appreciate your help. Thanks in advance!

 

[Jimmy]

Greetings Genesis,

You are correct. The best way to start out is calculating Rt. This is what's called a series-parallel circuit. You have to find the combined resistance of the two resistors in parallel and then add that to the value of R1. Rt=R1+1/(1/R2+1/R3). From there you can find total current which is the current through R1, by the way and the voltage drop on R1.

For two resistors in parallel, you can also use what's called the product over sum method. Rt=R1*R2/(R1+R2). That only works for two resistors in parallel, however.

Remember, for components in series, voltage divides and current stays the same. for components in parallel, current divides and voltage stays the same. After you find the voltage drop on R1, subtract that from Et (I use E for voltage) to find the voltage for the parallel part of the circuit. You'll notice that ER2 and ER3 are the same. You'll also notice that IR1 is equal to IRt. The total current has to flow through R1 because there is no other path for the current to flow. It splits, however, when it get's to the parallel circuit. The sum of the parallel currents will equal the total current.

 

[Genesis]

Thank you very much, Jimmy. I really appreciate your help. Your explanations were clear and straight.

Thanks again!