# Voltage between A and B

Can anyone explain to me how to calculate the voltage between A and B in this circuit please?

First, let the bottom node be GND. Then you have to realize that both voltage sources (batteries) are reversed in respect to each other. That means: $A>0,B<0$.

In the circuit you have two voltage dividers. One composed of the 25k and 47k, the other 10k and 33k.

Now, the rule of thumb for voltage dividers comes from Ohm's law. The voltage across a resistor is proportional to the current through that resistor. When you have two resistors in series, they share the same current. By rearranging Ohm's law for both R1 and R2, then substituting, you get the magical expression for voltage dividers:

$V_{mid} = V_{top} * \frac{R_{lower}}{R_{upper} + R_{lower}}$

Note that it only applies if there is no extra current drawn from the middle node.

Using that in your case gives the following:

• $V_A=100V*\frac{47k}{47k+25k}$
• $V_B=-100V*\frac{33k}{33k+10k}$

Then we simply subtract these from each other (in the desired order):

• $V_{AB} = V_A-V_B$

I'll leave the arithmetic as an exercise to the reader. Also, you might wanna lookup theory on voltage dividers.

I hope it's right...

• That should be $V_{AB}=V_A-V_B$ May 13, 2014 at 9:37
• Yes, you're right. Ill correct it. May 13, 2014 at 10:02
• This is NOT a 'complaint' but a comment. Your willingness to help them is appreciated and this is more a thought about how far you go on questions like this. The answer is arguably a bit too complete for a "homework type question". It's good to show them how, but the end result is almost "plug into calculator" level. While they may take your answer and learn from it, the essential Vmid = Vtop x Rlower/(Rupper + Rlower) is presented as a completed "black box" and may not be understood. MANY beginners have substantial trouble understanding this at first. Again - comment only. RM May 13, 2014 at 10:34
• @RussellMcMahon so how much of an answer is the "right" amount to give? Sounds like a classic case of "I'll know it when I see it" May 13, 2014 at 15:45
• @RussellMcMahon I see your point. However I personally prefer this example-driven teaching/learning. I believe that making someone force through the process of discovering a wheel doesn't necessarily teach him - simply because of the hatred of the subject. May 13, 2014 at 16:18