Hello,
The gate resistor is calculated from the power supply voltage minus
the gate forward voltage divided by the max gate current required for
proper operation.
For example, for this triac the max gate current is 10ma or 5ma if you
restrict the operation to certain quadrants. Lets say you want to go
with 10ma. Also, Vg max is 2v. This would mean
R=(V-Vg)/0.010
so with a power supply of 5 volts R would be:
R=(5-2)/0.010=300 ohms.
With a power supply of 10 volts,
R=(10-2)/0.010=800 ohms.
You can calculate the required resistance for any power supply voltage
this way.