Homework Help: HOw much power is drawn from a one volt battery?

1. Sep 12, 2010

jersey

1. The problem statement, all variables and given/known data

each bulb in the circuit has a resistence of one ohm. how much power is drawn from the one volt battery?

to see the circuit diagram, click on this link:

it is problem 16 on page 123

To see the circuit diagram, go here:
http://www.lightandmatter.com/bk4c.pdf [Broken]

GO to the link, scroll to page 123, and the diagram is problem 16.

2. Relevant equations

Ohms Law
Loop rule
Junction rule

3. The attempt at a solution

I have
D=B+E
A+B=C

and using Loop rule three times:
Va+Vc=1
Vd+Ve=1
Va=Vd+Vb

but i can't go on to solve the the five equatios cause i get lost. Can you help me?

Last edited by a moderator: May 4, 2017
2. Sep 12, 2010

Redbelly98

Staff Emeritus
Since you know the resistances, you can rewrite these in terms of the voltages.

For example, D = Vd/Rd, etc.

Shouldn't that middle equation be
Vd + Ve + Vf = 1​
?

3. Sep 12, 2010

jersey

regarding the middle equation, i assumed e anf F to be one single bulb with a resistance of 2 ohms.

I'm not sure how to re wrie each in relation to volatge like you say? Can you help?

4. Sep 12, 2010

jersey

P=V^2/R for each.

5. Sep 12, 2010

Redbelly98

Staff Emeritus
Okay.
Sure.
From Ohm's law, we know the current through bulb D is
D = Vd / Rd​
So we can replace D in the equations with Vd/Rd instead.
D = B + E​
we get
Vd/Rd = B + E​
Then do the same for B and E.

6. Sep 12, 2010

jersey

Ok, so my new equations are:
Vd/Rd=B+E
Which becomes
Vd/Rd=Bd/Rb+Ve/Re

7. Sep 12, 2010

Redbelly98

Staff Emeritus
Yes, good. Here are two more things to do:

1. Since you know what Rd, Rb, and Re are, you might as well put those numbers into the equation.

2. Do the same thing for the A+B=C equation.

After doing those, try to solve for the 5 unknowns Va, Vb, etc.

I'm logging off for the night, so good luck.

8. Sep 13, 2010

jersey

Substituting Rd, Rb and Re = 1 into equation gives:
Vd/1=Bd/1+Ve/1

A+B=C
becomes ?

sorry, I'm trying!

9. Sep 13, 2010

Redbelly98

Staff Emeritus
Okay, let's work some more with that equation before moving on.

Doesn't Re=2, since you have combined e and f into one single bulb with a resistance of 2 ohms?

What is "Bd"? I think you meant to write Vb there.

Also, a simpler way to write "Vd/1" would be ____?

10. Sep 13, 2010

jersey

Vd^-1

11. Sep 13, 2010

Redbelly98

Staff Emeritus
What? No. Look at these examples:

$$\frac{1}{1} = 1$$

$$\frac{2}{1} = 2$$

$$\frac{3}{1} = 3$$​

You're just dividing each number by 1, so you get the same number.

$$\frac{Vd}{1} \ = \ ?$$​

12. Sep 13, 2010

jersey

sorry Vd/1 is the same as Vd

13. Sep 13, 2010

jersey

Vd=Vb+Ve

14. Sep 13, 2010

Redbelly98

Staff Emeritus
Almost. Just one little error to address:

15. Sep 13, 2010

jersey

Vd=Vb+2Ve

16. Sep 13, 2010

Redbelly98

Staff Emeritus
No, try again. Look at what you wrote in post #6.

I'm logging off for the night but will be back online tomorrow.