Series: The same amount of current flows through each component. The voltage drop on each component is determined by the resistance (or reactance for AC) of the component. Parallel: The same amount...
Kirchoff's voltage law: In a series circuit, the signed sum of the voltage drops around the circuit add up to zero. Since a parallel circuit (just the two components of the parallel circuit) also...
In a simple parallel circuit -- for example, two resistors in parallel with a voltage source -- the voltage across the terminals of each component is the same. The current, however, 'splits' in order...