DC Circuit, and Similtaneous Equations?

Question

This if from my ITT Tech Math book, It makes absolutely no sense to me due to the fact that this class never went over ohms law or anything like that.

I tried my best to put it completely in a jpeg.
http://img.photobucket.com/albums/v371/MarkTivyn/sl3.jpg

How do i do this?

5000V should be 5000ohms

Answer 1

Rt - Total resistance.
R1 - Resistor 1.
R2 - Resistor 2.
ì1 - Current 1.
ì2 - Current 2.
ì3 - Current 3.
║ - Parallel.

From the circuit given:
Rt = R1║R2
Rt = (R1*R2 )/(R1+R2)
Rt = (3k*5k )/(3k+5k)
Rt = (15k )/(8k)
Rt = 1∙875kΩ

ì1 = V/R1
ì1 = 10V / 1∙875kΩ
ì1 = 0∙0053333....
ì1 = 5∙3333....mA.

ì2 = ì1[R1/(R1 + R2)]
ì2 = 5∙3333....mA[3k/(3k + 5k)]
ì2 = 0∙002
ì2 = 2∙0 mA.

ì3 = ì1[R2/(R1 + R2)]
ì3 = 5∙3333....mA[5k/(3k + 5k)]
ì3 = 0∙0033333...
ì3 = 3∙3333...mA

Answer 2

The effective resistance of two resistors in parallel is product over sum Thus the resistannce is (3000*5000)/8000=1875.
Since I= E/R we get I1 = 10/1875 = 0.0053333 amperes.
The current I2 = 10/3000 = .0033333 amperes.
The current I3 then is I1-I2=.002 amperes

Answer 3

All I do is remember that the voltage is constant along wires, and current is conserved. So, the voltage drop through both resisters is 10 V. Imagine that you replaced both resisters with one resister and conserved current, then:

v/r1 + v/r2 = v/R

now solve for R, the equivalent resistance.

1/r1 + 1/r2 = 1/R

If you just remember simple consevation and equalence conditions you don't need to memorize equations.

Answer 4

the Voltage is the same over both resistors so the current in each is
i1=10/3000 [A], i2=(10/5000) [A]
i3= i1+12= (1/300+1/500)[A] = 5,33mA

Answer 5

The question is notably obscure. besides, u will in undemanding terms have differential equation for transients in DC circuits. For stable state u won't have a differential equation. So how come u opt for us to help u devoid of even understanding what u opt for.

Answer 6

i=v/r

10/3k= .003333333333
10/5k= .0020000000

.002+.0033333=.005333333

or from the equations in answer #2

1/3k+1/5k = 1/circuit impedence

circuit impedence = 1875 ohms

10v/1875Ohms = .0053333333 Amps