Voltages in series and parallel circuits

Law of additivity for voltages in series

In a series circuit (where the dipoles are connected one after the other, with a single path for the current), the total voltage supplied by the generator is equal to the sum of the voltages across each dipole:

U_generator = U1 + U2 + U3 + ...

Example: a 9 V generator powers two identical lamps in series. If they share the voltage equally, each receives U₁ = U₂ = 4.5 V, and we can verify that U₁ + U₂ = 9 V.

Law of Voltage Equality in a Shunt Circuit

In a branch (or ‘parallel’) circuit, several branches are connected to the same two nodes. In this case, all dipoles placed on the branch circuits have the same voltage across them, equal to the voltage of the generator:

U_generator = U1 = U2 = U3 = ...

Example: a 6 V generator powers two lamps in a shunt configuration. Each lamp receives U = 6 V directly across its terminals, regardless of the number of branches.

Summary table

Circuit configuration	Relationship between voltages
Series	U_generator = U1 + U2 + ... (voltages add together)
Shunt	U_generator = U1 = U2 = ... (the voltages are equal)

Common pitfalls to avoid

• In a series circuit, do not forget that you must add up all the voltages, not just two.
• In a shunt circuit, do not assume that the voltage is ‘shared’ between the branches: each branch receives the full voltage from the generator.
• Always check the type of circuit (series or shunt) before applying the correct rule.