Determine the difference in potential between A and B

[Cade]

Homework Statement

Determine the difference in potential between A and B.

Homework Equations

Kirchhoff's rules for current (loop, junction), V = IR

The Attempt at a Solution

I have found the currents through the resistors:
12 - 3.9a - 1.2b - 9.8a = 0 (loop rule)
12 - 3.9a - 6.7c - 9 - 9.8a = 0 (loop rule)
a = b + c (junction rule)
c = -1.0295 & b = 1.75196 & a = 0.722456

6.7 ohm resistor has 1.02 A counterclockwise
3.9 ohm and 9.8 ohm resistors have 0.72 A clockwise
1.2 ohm resistor has 1.7 A clockwise.

What do I do from here? I know that if A and B were in series, the difference in potential between them would be a drop which equals the potential differences across each component between them in series, but this is in parallel, and so I don't know what to do.

 

[gneill]

Kirchhoff's voltage law works for any components along a continuous path. If you can trace a path from B to A and can add up all the voltage changes along the way, you're done!

 

[Cade]

There is a 1.2 ohm resistor on one path between A and B, and the current through it is 1.7 A, so the potential difference across the resistor is 2.04 V. Is this the difference in potential between A and B? The correct answer is 2.2 V.

 

[gneill]

There is a 1.2 ohm resistor on one path between A and B, and the current through it is 1.7 A, so the potential difference across the resistor is 2.04 V. Is this the difference in potential between A and B? The correct answer is 2.2 V.

Your method is correct.

If you keep a few more decimal places in your intermediate values you should find that the voltage is a bit higher than what you got (although not quite 2.2 V).

You could also try the same thing for other paths between A and B.

 

[Cade]

1.2 ohms * 1.75196 A = 2.102352 V

Still coming up short.

Using the other available path,
-6.7*1.0295 + 9 = 2.102352 V

Hmm... I suppose it's close enough.

 

[gneill]

1.2 ohms * 1.75196 A = 2.102352 V

Still coming up short.

Using the other available path,
-6.7*1.0295 + 9 = 2.102352 V

Hmm... I suppose it's close enough.

Not only is it close enough, 2.1V is the correct answer! Sometimes books can be, shall we say, not entirely correct.

 

[Cade]

Got it, thanks for your help.