pwillard:
With an NPN transistor, you normally want the Emitter closer to ground potential for maximum transfer. And you ALWAYS want to limit transistor Base current with a resistor to prevent abusing the transistor or what is controlling it...
in the circuit you posted, you're switching on via the 5v base, but the collector/emitter sit on 12v/0v
what if, you only had 10ma to play with at 5v
but, you have a 2nd 12v rail of 3amps.
collector to 12v, emitter to your relay (with reverse diode protection) , when the 5v switches on the transistor, your relay would not fire off, because it's 12volts
but, let's supposing it was rated 5v and requires 100ma to switch the relay on...
using the above method, the relay would switch on as it consumes 100ma from the 12v rail but supplys only 5v energizing your relay.... I don't get the physics,,, i guess i'll just have to accept i understand the principal not so much how it works .