Mike: Yes, there are other ways to wire your circuit with the switches. Placing the resistor in other places will change the calculation.
LEDs wired in series is close to what we've looked at before. Now you just add the forward voltage (Vf) of each LED before subtracting the supply voltage and dividing the whole mess by the forward current (If). Here we just multiply the forward voltage by the number (n) of LEDs in series:
R = (Vs - (Vf * n)) / If
R = (12 - (3.3 * 2)) / .02
R = (12 - 6.6) / .02
R = 5.4 / .02
R = 270 Ω
To wire 2 LEDs in parallel using 1 resistor for them both, you take the desired forward current (If) of the LEDs and multiply by the number of LEDs (n). Again we'll use 20mA as the target current.
R = (Vs - Vf) / (If * n)
R = (12 - 3.3) / (.02 * 2)
R = 8.7 / .04
R = 217.5 Ω
However, parallel wiring of 2 LEDs from the same resistor is not recommended. Here's a note from this calculator page that warns about brightness variations.
Note: You should avoid connecting LEDs in parallel with just one resistor shared between them. Identical LEDs can be successfully connected in parallel, but each LED may have a slightly different voltage drop, and the brightness of the LEDs will differ. If you want to connect the LEDs in parallel each one should have its own resistor. Calculate the value for a single LED and connect all the LED-resistor pairs in parallel.
I hope that helps.
