Figure 1.  Circuits for driving LED's directly from the AC line

Figure 1 shows two circuits that can be used to drive LED's directly from the AC line without a need for a transformer-based DC supply.

Both circuits employ a series non-polarized capacitor to achieve a large voltage drop that causes the LED's to see a lower voltage across them.  A 1-K series resistor  is also used to limit the current  through the circuit, especially during the periods when the capacitor is minimally charged and acts like a short circuit.

For this circuit to work properly, the capacitor must conduct current in both AC directions to prevent it from becoming fully charged permanently and causing the circuit to become open. This is the purpose of the 1N914 diode in the first circuit - to provide a current path during the negative cycle.  It also limits the reverse voltage across the LED.  The LED lights up during each positive cycle.

In the second circuit, the ordinary diode is replaced by another LED that lights up during the negative cycle to complement the one that lights up during the positive cycle.

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