Two bulbs of different wattage in one AC circuit
Parallel
All the mains bulbs in your house are probably in parallel so that should satisfy you that that works. Each lamp will draw the current it requires. 







simulate this circuit &ndash; Schematic created using CircuitLab

Figure 1. Your house wiring. This system works well because the lamps are fed from a constant voltage supply.

Let's do some easy maths using a 100 V supply. \$P = VI\$, where P is power, V is voltage and I is current. Using Ohm's law, \$ V = IR \$ we can modify the power formula to get \$ P = I^2R = \frac {V^2}{R} \$. Rearranging the last one gives us \$ R = \frac {V^2}{P} \$. This is hot\$^1\$ filament resistances were calculated.

Series connected similar lamps

If you put equal lamps in series they will divide up the available voltage between them and the current will be \$ \frac {1}{n} \$, where n is the number of lamps.\$^2\$







simulate this circuit

Figure 2. In this circuit both lamps have the same resistance so will drop half the supply voltage across each. Since the total resistance is doubled the current will also be halved. Since P = VI then the each lamp will be running at 1/4 power.

Series connected dissimilar lamps







simulate this circuit

Figure 3. More voltage is dropped across the higher resistance / lower wattage lamp. It will glow the brightest.

If you put unequal lamps in series the one with the highest filament resistance will limit the current to the others. It may also glow the brightest (if they're all the same voltage rating).

Power calculation for each lamp:


100 W: \$P = \frac {V^2}{R} = \frac {33^2}{100} = 11~W\$.
50 W: \$P = \frac {V^2}{R} = \frac {67^2}{50} = 22~W\$.


Note the possibly surprising result that the lower powered lamp will be brighter and consume more power.



\$^1\$ Lamp filament resistance increases dramatically with temperature. I have not factored this into the calculations.

\$^2\$ Again, the current calculation will be higher than calculated here because the filament resistances will be lower when cold.