Why id voltage different in series circuits and the same in parallel circuits?

Answer 1

Parallel circuit: The fact that the voltage is the same follows from Kirchoff's Voltage Law.

Series circuit: The voltages of the individual resistances must add up to the total voltage. This, too, follows from Kirchoff's Voltage Law. If the resistances have the same values, all of them will drop the same voltage (which, of course, will be less than the total resistance). But if they are different, Kirchoff's current law tells us that the same current must flow through each resistor in series - and the voltages will be different in this case, according to Ohm's law.

Answer 2

Series circuit: Current must be the same by Kirchhoff's Current Law. Basically, if the current has nowhere else to go, then the current that passes through one element will continue through the next.

Parallel circuit: Voltage must be the same, by Kirchhoff's Voltage Law. This is related to the Law of Conservation of Energy - and the fact that electrical forces are conservative forces. Thus, the voltage between two points in a circuit is the same, no matter what path is taken. Voltage is energy per unit charge; and this behavior is the typical behavior for conservative forces.