Help on determining voltage differences (basic circuit theory)

Question

I am trying to reteach myself basic circuit theory using "Practical Electronics for Inventors 3rd Edition" by Scherz and Monk.

I am working an example in which it asks to calculate the voltage difference between a variety of points (I have included a diagram below. Please note that I could not find the typical ground symbol I'm used to , so I had to use the one provided under the name GND). The example asks to find the voltage difference between points: A and C (denoted as V[sub]AC[/sub]), B and D, A and D, and B and C. Now the book lists the voltage difference between A and C as plus +3 volts and the voltage difference between A and D as +12 V, then turns around and lists the voltage between B and C as +9 volts.

I don't see how they are getting the figure for the voltage between B and C (I keep calculating -9V by the way the other two voltages were calculated).

^{simulate this circuit – Schematic created using CircuitLab}

Answer 1

You're entirely correct. \$V_{BC} = -9V\$

Re-arranging the schematic may make it more clear. Voltage difference from A to C is 12V - 9V = 3V because BAT2 is pointed in the same direction we're traveling from A to C.

The book probably just made a typo and meant \$V_{CB} = +9V\$. Note that typos are quite common in many textbooks I learned from. Be especially wary of first editions. They haven't had a bunch of students/professors sending in all the corrections yet in the first editions. You would hope by the third edition, someone would have cared enough to fix it.

^{simulate this circuit – Schematic created using CircuitLab}