Why outlets spark when unplugging - EMF & Inductors

An easier way to understand: let's say the switch goes from fully engaged to completely disengaged in a short but finite amount of time. Let's evaluate the boundary conditions: when the switch is fully engaged, there is current through the circuit, supporting the magnetic field. When the switch is fully disengaged, there is no current through the circuit, and therefore no magnetic field. Now that means all the energy has to be dissipated in the finite amount of time. 

The resistance of the circuit, in other terms, basically describes how much power you burn given a voltage across it. Since the energy has to dissipate rather quickly at a rate that exceeds the original rate of dissipation (= voltage of the power source), it logically means that the voltage has to rise to meet the power dissipation speed.