Answer
See answers.
Work Step by Step
a. The filaments can be connected individually or in parallel. The voltage across each filament is 120V in every situation.
Power $P=V^2/R$. For the 50-watt output, only the higher-resistance filament should be used. For the 100-watt output, only the lower-resistance filament should be used. When both filaments are connected in parallel, the output will be 150 watts.
b. Find the lower resistance.
$$P=\frac{V^2}{R}$$
$$R=\frac{V^2}{P}=\frac{(120V)^2}{50W}=288\Omega$$
Now find the higher resistance.
$$P=\frac{V^2}{R}$$
$$R=\frac{V^2}{P}=\frac{(120V)^2}{100W}=144\Omega$$
