A simple way to add turn-on and turn-off delay to an LED circuit is to connect a resistor and capacitor in series to form an RC circuit. It takes time for a capacitor to charge/discharge through a resistor. The time is determined by T = R x C, where R is the resistance in ohms, C is the capacitance in Farads and T is time in seconds. The value of RC is actually the time it takes for the capacitor to be charged to 63 percent of the supply voltage.
Calculate the resistance and capacitor values based upon the desired delay time. For example, assume the supply voltage is 3 volts, the LED forward voltage is 2 volts and the current through the LED will be 10 milliamps. Then the LED forward voltage will be close to 63 percent of the supply voltage. If we use a 300 ohm resistor and 10,000 microfarad capacitor, there will be a delay of approximately 3 seconds (RC = 300 ohms x .01 Farad) after the power is applied before the voltage at the junction of the resistor and capacitor is equal to the LED forward voltage.
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Connect one lead of the 300 ohm resistor to the power strip at the top of the breadboard.
Connect the other lead of the 300 ohm resistor to the positive lead of the capacitor.
Connect the negative lead of the capacitor to the ground strip at the bottom of the breadboard.
Connect the positive lead of the LED to the point where the capacitor and resistor are connected.
Connect the negative lead of the LED to the 100 ohm resistor.
Connect the other lead of the 100 ohm resistor to the ground strip.
Connect the negative (black) lead of the battery holder to the ground strip.
Connect the positive (red) lead of the battery holder to the supply strip. There should be a delay of approximately 3 seconds between the time you connect the red lead and the time the LED turns on.
Remove the red lead of the battery holder from the supply strip. There should be a shorter delay of approximately 1 second between the time you remove the lead and the time that the LED turns off.