# Difference in voltmeter reading for series circuit and parallel circuit

Assume that we have two components, R1 and R2, that we wire in series. Assume that the voltage across R1 is 10 V, and the voltage across R2 is 30 V.

We can illustrate this case with the following image:

If we now wire a voltmeter in parallel over both components, between the points marked A and B in the image, the voltmeter will then show the potential difference as 10 V + 30 V = 40 V.

Now assume that we wire the two components in parallel as shown in the image below:

We now assume that we adjust the current, and add some other components to the two branches, so that the voltage across R1 yet again becomes 10 V, and the voltage across R2 yet again becomes 30 V.

If we then wire a voltmeter between the points labeled A and B on this image, the voltmeter will then show the potential difference as 30 V - 10 V = 20 V.

What is the intuition as for why we subtract the two values in the second scenario? I know how to do the calculations, but I struggle a bit to intuitively understand why the voltmeter will not show 40 V in the second case as well.

• Do you know Kirchhoff's voltage law? Commented Apr 26 at 17:51
• Yes, I know Kirchhoff's laws, Ohm's law, the resistance formulas, etc. I am able to do all calculations in every circuit problem I encounter. I am really just trying to get the intuition as to why the voltmeter will show 40 V in the first example, but 20 V in the other example, even though, in both cases, the voltmeter spans both components. Commented Apr 26 at 17:52
• So sum the voltages around the loop made up of the two resistors and the voltmeter per Kirchhoff's law. What do you get? Then do the same in the first example. Note the voltage polarity across each resistor between the two examples. Commented Apr 26 at 18:11
• Ah, thanks. Now it make sense! Beacause the two branches form a loop, the net sum of the voltages must be zero. Thus, one of the branches will yield a negative value for the voltage, and that is why we get a difference of 20 V. Commented Apr 26 at 18:17