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Electricity and MagnetismI

Voltages in Series Circuits
........

Consider the simple series circuit above.

Energy lost by each Coulomb of charge moving from A to B is V₁.

Energy lost by each Coulomb of charge moving from B to C is V₂.

Energy lost by each Coulomb of charge moving from C to D is V₃.

Obviously the total amount of energy lost by each Coulomb of charge moving from A to D must be V₁ + V₂ + V₃ (= V).

Conclusion

The total voltage across components connected in series is the sum of the voltages across each component. Note that the validity of this statement does not depend on what the components are.

Voltage across Components in Parallel

All points inside the dotted ellipse on the right must be at the same potential as they are connected by conductors assumed to have negligible resistance.

Similarly for all points inside the dotted ellipse on the left.

So the three voltmeters are measuring the same voltage.

Conclusion

Components connected in parallel with each other all have the same voltage.

Again, this does not depend on what the components are.