Arduino as an alarm sensor

I'm building an Arduino based alarm monitor. I have normally closed door sensors installed and wired to my Arduino.

5v -> door sensor -> digialPin

Normally the circuit is closed. Do I need a resistor between 5v and the digital pin? When a digitalPin is set to INPUT it seems to have a pretty high resistance?

put a pull up/down resistor between digital and ground 10k i beleve... its much like a button

I have a pulldown resistor on the digital pin already. I guess that makes my diagram

5v → door sensor → digitalPin & 10k grounded resistor

i think thats it then... then you digital read it, and make it do dome sort of alarm...

I was trying to be efficient. No sense in have a closed circuit that's pumping a bunch of electricity through it. Would a resistor in-live save me some electricity, and maybe a little heat?

Or is it unnecessary?

if i understand correctly, there is only power flow if the door is open?

Reversed... there is electricity flow when the doors are closed (which is most of the time).

Part of the reason I asked is because if I put an LED inline with the door sensor and input pin it lights up really dim. It's like there is some sort of internal resistance on the digital pins.

Does your door sensor use a magnet on the door jam and a reed switch on the actual door. If so its just like wiring up a pushbutton.