GeorgeL, don't you have your arrow on the transistor backwards? It should be an NPN, right?Wouldn't you want to use a 555 timer IC to do it? Make pin 3 drive one transistor each for each relay via a 100 ohm resistor.
ljcox, you are right when you see the switch closed. But when it is opened, that is a voltage divider in there.
Miles, I agree that adding a resistor in series does not lessen power used. Ohms law says E=IR and power of course is VA in watts. For a given voltage and a given resistance in a circuit, current I would be V/R. By increasing R,I will fall but the voltage across the series resistances goes up. So, I goes down but E goes up inversely proportionally. Since power if VA, it remains the same. Only switching will reduce power consumption like the scr speed controller for small DC motors where the SCR is oscillating. I would stand corrected if I am wrong.