2 Way lightbulb with different power

[t_n_p]

Homework Statement

A 3-way lightbulb can produce 50W, 100W or 150W at 120V. Such a bulb contains 2 filaments that can be connected to the 120V individually or in parallel.

a) describe how the connections to the 2 filaments are made to give each of the 3 wattages

b) What can be the resistance of each filament?

The Attempt at a Solution

I'm really not sure where to start

 

[mjsd]

equation: P=VI=V^2/R
obviously, for two filaments (ie. two resistances), you can make the following combo (if R1=R2)

1. R1//R2 (parallel)
2. R1 (by itself) or R2 (by itself)
3. R1+R2 (series)

with effective resistance of case 1 < case 2 < case 3

you got it now?

now if case 3 (in series is not allowed then) you will have to assume that R1 not equal to R2 to get three cases

 

[t_n_p]

Ok, so using P=V^2/R

For the 50w wattage, V is constant at 120V, P=50W.
Subbing into the equation, R=288ohms

For the 100W wattage, subbing into the equation, R=144ohms

For the 150W wattage, subbing into the equation, R=96ohms

but how do I know if they are connected individually or in parallel?
I'm a massive physics noob, go easy on me!