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## Homework Statement

I attached a screenshot of the problem(s) that my professor gave in a practice exam.

## Homework Equations

∑I = 0 at each junction

∑V = 0 at each closed loop

P = I

^{2}R = V

^{2}/R

R

_{series}= R

_{1}+ R

_{2}+...

## The Attempt at a Solution

Part A:

I think the current I in the center, broken line of current, is zero because that wire is broken. Then

I

_{1}+I

_{2}= 0. So I

_{1}= I

_{2}= I

Going around the large loop, starting from the battery at the top:

V + V - IR - IR = 0

2V = 2IR

V=IR

12 = I(10)

I = 1.2

In the bottom loop...

V

_{a}+ V - IR + V = V

_{b}

V

_{a}- V

_{b}= -2V + IR

V

_{a}- V

_{b}= -2(12) + (1.2)(10)

V

_{a}- V

_{b}= 12V in absolute value...

Is absolute value what I'm looking for? +12V is the answer in the solutions my professor provided.

Part B:

R

_{series}= R

_{1}+ R

_{2}+...

R

_{series}= 10 + 10

R

_{series}= 20

P = I

^{2}R = V

^{2}/R

P = (1.2)

^{2}(20) = 28.8W

P = (12)

^{2}/(20) = 7.2W

These aren't equal. I tried it with R in parallel as well (R

_{eq}= 5), and it's still wrong. In the answers provided each of the power equations are multiplied by 2 and R = 10. Why is all of this?

Thanks!