That circuit will be fine for one relay, but may not work as expected with 2 or more relays.
Consider this...
1. Doug's relay wants 40ma @ 5VDC. (It will work at less voltage and current but may not reliably operate)
2. 6.3VAC and a bridge will produce 8.9VDC unloaded. (Let's call it 9V to make the math easier)
So, we need to drop 4 volts across the resistor. Using a 100Ω resistor will do this nicely and will allow 40ma to flow (I = 4V\100Ω = 40ma). Thats perfect for one relay coil.
Now add a second relay. Each relay wants 40ma for a total of 80ma. This 80ma must flow thru that 100Ω resistor. The resistor will now drop 8 volts (.08ma X 100Ω = 8V) That only leaves 1V for the relays.
Add a third relay and the relays now want a combined total of 120ma. The resistor will try to drop 12 volts, but we only have 9 volts on tap. So, current will have to drop and this will probably drop well below the point to energize three relays.
The answer is to use a resistor that can automatically adjust it's resistance to compensate for different relay current requirements. That sounds like a series voltage regulator. A three terminal 5 volt regulator is the perfect solution and only costs $2 at RadioShack.
This is how I'd do it... Remove the 100Ω resistor and the bottom 4700µF cap. Install a 7805 regulator, input connects to the positive of the cap, common (or reference) connects to the negative side of the cap, and the output becomes your +5VDC that connects to the relay coil. And now you don't have to be concerned with how many relays you try to energize simultaneously. (Within reason of course. That $2 7805 regulator is good for one amp, or 25 each 40ma relays, so don't exceed that.

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