Why is current the same everywhere in a circuit? (DC) In a series circuit, the voltage is the same everywhere on that circuit. However, thinking about Voltage as a steady force or potential, I imagine that at parts of the circuit without resistance, the current would be greater as the force would be able to move them faster, without any obstruction. Why is this not the case?
 A: Voltage is not the same throughout all the elements in a series circuit. The sum of all the voltage drops across all the series elements is always equal to the source voltage.
The charge carriers flowing through a series circuit are conserved- there is nowhere else for them to go except in the circuit loop, and this means all the charge carriers exiting one circuit element enter the next one, and so on all the way around the complete circuit loop.
This means the current flowing through all the individual circuit elements in series is the same.
A: The situation is completely analogous to that of a water pipe of uneven thickness (horizontal, so we can ignore gravity), with voltage being analogous to pressure.  If the current through any part "tried" to increase (compared to the current in a neighboring part), it would create a buildup of charge (water molecule concentration in our pipe analogy), which would alter the voltage (pressure) gradient and make it slow down again.
For that reason a condition of unequal current can't persist for too long. Which means that in the normal, steady state situation (same current everywhere), the voltage (pressure) gradient varies along the path, to "enforce" the condition of the equal current in order to "compensate" for the fact that it's easier for the current to flow through some parts (low resistance/wider pipe) than through others.
