Current and power in restisor combo

[hitman0097]

Homework Statement

The battery in the figure below has negligible internal resistance.

(a) Find the current in each resistor.
3 ohm resistor-
4 ohm resistor-
2 ohm vertical resistor-
2 ohm diagonal resistor-
(b) Find the power delivered by the battery.

Homework Equations

Loop Rule, Junction Rule, Resistor Rule. ?
P=VI=RI²=(V²/R)
R=V/I
I=V/R
Req=(V₁+V₂/I)

The Attempt at a Solution

6/3=2A 6/4= 1.5A, 6/2=3A ect. all wrong
For I₁: -3omhs (since it's along the current) I₁-2omhs(along current)I₁+6V=0 solving for I₁=1 wrong
Am I leaving stuff out?

 

[cepheid]

You tried to use the loop rule for the loop involving the 3 ohm and the vertical 2 ohm resistor only. It didn't work because the loop is not a closed, isolated loop. After the current has passed from the positive end of the battery through the 3 ohm resistor, it has the option of going into three different branches. Therefore, the current in the 3 ohm resistor is not the same as the current in the vertical 2 ohm resistor. That's why the loop rule didn't work.

But I did just give you a hint about the arrangement of the vertical 2 ohm, diagonal 2 ohm, and 4 ohm resistors that should make this problem easy.

 

[hitman0097]

Isub1(-3ohms-2ohms-2ohms-4ohms)+6V=0 Solve for I=.55A Current only changes at intersections so all the current has to pass threw the 3 ohms then branch into 3 parts it reconnects with the 2 diagonal and the 4 ohms then they reconnect with the 2 vertical. Which must equal the incoming current? right. I think I get the idea it's just the setup that is confusing me a bit.

 

[dreamspace]

Hey, first of all, I'd start with finding the Main current I.

The 2 ohm(R2), 2 ohm(R3) and 4 ohm(R4) resistors are all in parallell with each other, and in serial with the 3 ohm (R1), so:

R1 + (R2||R3||R4) = R_tot
3 ohm + ((1/2 ohm)+(1/2 ohm)+(1/4 ohm)) = 3.8 ohm

You'll find the current via I_tot=E/R_tot => 6 volt / 3.8 ohm = 1.58A

From there, you can use current divider to find the current going through each resistor(if you don't know what current dividing is, there's a good article on wikipedia)

I_r1 = 1.58A (the whole main current is going through it)
I_r2 = 1.58A * ((2 ohm||4 ohm)/((4 ohm||2 ohm) + 2 ohm) = 0.632A
I_r3 = 1.58A * ((2 ohm||4 ohm)/((4 ohm||2 ohm) + 2 ohm) = 0.632A

I_main - I_r2 - I_r3 - I_r4= 0
I_main - I_r2 - I_r3 = I_r4
1.58A - 0.632A - 0.632A = 0.316A

Power delivered by the battery => P=UI => 6v*1.58A = 9.48 W

Hope I could help, cheers.

 

[hitman0097]

Thanks, I asked my professor and he gave me that same method.