Find the potential difference of point b relative to point a

[Snazzy]

Homework Statement

Find the potential difference of point b relative to point a.

Homework Equations

The Attempt at a Solution

I found out that E1 = 18V and E2 = 7V but I don't know where to go from there.

 

[The Electrician]

Voltages are measured with respect to some reference. What did you use for your reference to get E1 = 18V and E2 = 7V? If these were correct, then the potential DIFFERENCE would be 18-7 = 11 volts, but it isn't.

All you need to do is look at the top branch. The current in the branch is given, so the voltages across the two resistors are known. Combine that knowledge with the value of the voltage source in the branch, and you should be able to get the DIFFERENCE in potential (voltage) between point a and point b.

 

[Snazzy]

Ok, so the potential difference across the 1.00 Ohm resister is 1V, so the potential at A would be 20-1 = 19V, and then the potential difference across the 6.00 Ohm resistor is 6V, so then the potential at b would be 0+6 = 6V.

So then Vb - Va = -13V?

Also, how would I do that question? I've deduced the currents in each branch.

 

[The Electrician]

The -13 volts is correct.

When you say "...so the potential at A would be 20-1 = 19V...", you are using the unlabeled point between the 20 volt battery and the 6 ohm resistor as your reference (ground?). You didn't mention it, but you should be aware when you make such a choice. Remember that voltage is always a relative thing; you must measure or compute with respect to some reference point. I would have chosen point a as my reference because the question wants to know the voltage at point b RELATIVE to point a. This makes point a the logical reference. But since the question wants to know the DIFFERENCE in voltage between point a and point b, any point in the circuit can be the reference because it will fall out of the equation when the difference is taken.

For the next problem, if you know the currents, then moving from point a to point b, multiply the current in the top branch by the 3 ohm resistor to find the voltage across that resistor. Multiply the current in the second branch by the 4 ohm resistor to find the voltage across that resistor. Then the voltage between point a and point b will be the sum of the voltages across the 3 and 4 ohm resistors, taking into account the polarity of each voltage.

 

[Snazzy]

Still a bit lost. The current in the top branch is 0.4A, which means if I multiply by the resistance, the potential difference across the 3 Ohm resistor is 1.2V.

The current in the middle branch is 1.6A, which means if I multiply by the resistance, the potential difference across the 4 Ohm resistor is 6.4V.

Now how do I take the polarity of the voltages into account? The voltages of the batteries or the voltage differences?

 

[The Electrician]

You've got take into account polarities of batteries and also voltages across resistors. You need to know the direction of the current in each branch to determine the polarity of the voltage across the resistors. Then end of the resistor where the current enters is by convention positive.

 

[Snazzy]

Oh okay. The current in the top branch is traveling from the left of A to the right of the 3 Ohm (from what I found using Kirchhoff's laws), so then at point A, the polarity is positive. And the current is traveling from the right of the 4 ohm resistor to the left of B (again, from what I found using Kirchhoff's law), so then the polarity at B is negative.

So then if I'm trying to find the potential at point A, relative to B, Va - Vb = 1.2 - (-6.4) = 7.6?