Ohm's Law and the Principles of DC Circuits

[tigerwoods99]

Homework Statement

R1 = 9.29 V= _____ I = _______
R2 = 9.19 V= _____ I = _______
R3 = 8.45 V= _____ I = _______
R4 = 4.47 V= _____ I = _______
R5 = 9.12 V= _____ I = _______
R6 = 4.60 V= 9.15 v I = 1.99 a

1/(r1, r2, r3) = (1/R1+R2) + (1/R3) = 5.7986 equivalent for R1, R2, R3
1/(r4, r5) = (1/R4) + (1/R5) = 2.9997

Picture is attached. How do I got about finding these terms:

Homework Equations

1/(r1, r2 ...) = (1/r1) + (1/r2) ...

V = IR

The Attempt at a Solution

 

[tiny-tim]

hi tigerwoods99!

1/(r1, r2, r3) = (1/R1+R2) + (1/R3) = 5.7986 equivalent for R1, R2, R3
1/(r4, r5) = (1/R4) + (1/R5) = 2.9997

Yes, those are the correct formulas (I haven't checked the actual numbers).

How do I got about finding these terms:

Homework Equations

1/(r1, r2 ...) = (1/r1) + (1/r2) ...

I don't understand what you're asking …

you have the equivalent resistances, so find the currents, and then find the voltages.

 

[tigerwoods99]

I am not sure how to get from equivalent resistances to currents...

 

[tiny-tim]

I am not sure how to get from equivalent resistances to currents...

First add all the equivalent resistances to get the total equivalent resistance for the whole circuit.

That will give you the current, I₆, in the undivided part of the circuit.

Then write down the Kirchhoff's rules equations for the other currents, I₁₂ I₃ and I₄₅ (one equation for each junction, and one for each loop) …

what do you get? ​

 

[Tommo1]

Simplify the circuit...
R4||R5 = 3.00 ohms
(R1 + R2)||R3 = 5.80 ohms

Then work back through the circuit using the voltage divider...
V1/VT=R1/RT
This gives R4||R5 = 5.97 V (They both have this voltage as they are in parallel)

To get the currents use the current division equation I1 = IT X R2/RT.

You then repeat this process for the (R1 + R2)||R3 part of the circuit.

 

[tigerwoods99]

we havn't learned about capacitors, all we go is like:

V = IR
Vt = v1 + v2...
It = i1 + 12..
(1/r(x)) = (1/...) + (1/...)

I got I6 done:

R1 = 9.29 V= _____ I = _______
R2 = 9.19 V= _____ I = _______
R3 = 8.45 V= _____ I = _______
R4 = 4.47 V= _____ I = _______
R5 = 9.12 V= _____ I = _______
R6 = 4.60 V= 9.15 v I = 1.99 a

 

[tigerwoods99]

Simplify the circuit...
R4||R5 = 3.00 ohms
(R1 + R2)||R3 = 5.80 ohms

Then work back through the circuit using the voltage divider...
V1/VT=R1/RT
This gives R4||R5 = 5.97 V (They both have this voltage as they are in parallel)

To get the currents use the current division equation I1 = IT X R2/RT.

You then repeat this process for the (R1 + R2)||R3 part of the circuit.

How did you get R4||R5 = 5.97 volts?

 

[tigerwoods99]

Please HElp!

 

[Tommo1]

Here's how to do it using only V=IR and series and parallel resistors.

Combine R4 and R5 in parallel
1/Rt=1/R1 + 1/R2
This gives Rt=3.00 ohms

Now add R1 + R2 in series = 18.48 ohms
Then combine that with R3 in parallel to give 5.80 ohms.

[PLAIN]http://www.xphysics.co.uk/x/E1.jpg

This is a series circuit so current will stay constant.

Finding the voltage across the 3 ohm resistor V=IR =1.99 x 3 = 5.97 V

Now expand that part back out...

[PLAIN]http://www.xphysics.co.uk/x/E2.jpg

Clearly V4=5.97 V and also V5 = 5.97 V.

The currents are I = V/R = 5.97/4.47 = 1.34 A for I4.
And similarly I5 = 0.65 A

Now go to the top part of the circuit and do the same process.

[PLAIN]http://www.xphysics.co.uk/x/E3.jpg

V3=11.54 V, I3=1.37 A

Then for the little series part...

[PLAIN]http://www.xphysics.co.uk/x/E4.jpg

V1=5.76 V, V2=5.74 V, I1=I2=0.62 A

Note that my current direction is "electron flow" and I'm using European resistor symbols.

There are lots of different ways of doing this sort of problem but this is a simple approach even if a bit long winded.

Hope this helps!