Analog circuit to turn on LED for 10 seconds just after power is applied?

Is it possible to use an analog circuit to turn an LED on for 10 seconds after 5v power is applied, then turn it off until power is removed and reapplied? This would be useful in small battery-powered designs; if a "power status" LED turns on for a short time after you've applied power, you are sure that the circuit is working...no need to constantly keep it on and drain more of the battery.

So, this is what the process would look like:

1. Plug power in



2. LED turns on


3. 10 second delay


4. LED turns off


5. infinite delay

Is there a simple analog circuit that can do this?

Update: Thanks for the help on this one. I agree that a single big cap and resistor solution would be too expensive/big to be practical. I think I'll use a MOSFET or some transistor array using Olin Lanthrop's schematic below.

Answer

Here is a circuit that should work (untested):

These are all cheap jellybean parts and will be together still significantly cheaper and smaller than a large capacitor to provide the LED current directly. The LED will also be on at full brightness for most of the time with a short, if any, soft off near the end.

D2 ensures that C1 is discharged when power is off. C1 therefore starts discharged when power is applied. C1 slowly charges thru R2 to provide the timing. Adjust R2 to get the desired LED on time. The value shown is a rough guess. Experimentation is required at these low currents.

Q1 is on as long as C1 is charged to below 4 to 4.5 Volts or so. Q1 turns on Q3, which turns on Q2, which turns on Q4, which turns on the LED. When C1 charges up high enough, Q1 turns off, turning off all the rest, including the LED. The LED current is set to about 10 mA in this example. Adjust R3 according to the desired LED current.

Leakage when off should be low enough to be ignorable. If not, add 1 MΩ resistors accross B-E of Q2 and Q4.