Halogen bulb/LED cluster swap

Hi all. Have been gone a bit but am back & still trying to blow myself up!

Converting a 12VAC 10VA line to run LED cluster. Original had an M11 size 5ω halogen bulb. Should be no problem, right? 4 diodes & a capacitor (see attachments).

Question: is there a good rule of thumb for determining an appropriate capacitor in simple circuits? For this one I chose a value based on research. I'd prefer to be able to compute a value without necessarily using tangent & cosine equations .

Suggestions?

The capacitor will quickly charge to 16.8V.
the value of the capacitor depends on how much ripple your circuit can tolerate.

If Vm is the peak voltage of the secondary and Vr is the ripple voltage then Vdc will equal:

Vdc=Vm-Vr/2

and

Vr=Idc/(2*f*C) or Vr=Vdc/(2*f*C*R)

Vr=peak-peak ripple voltage
Idc=dc current the load draws
Vdc=dc voltage across the load
f=mains frequency
C=filter capacitor value
R=resistance of the load

Note that the above equations give approximations of the voltages but close enough.