Question

If a current of 0.5 A flows in a 75 W light bulb when the voltage difference between the ends of the filament is 150 V, what is the resistance of the filament?

Answer 1

Power is current times voltage.  Using Ohm's Law V=IR, we can express power in two additional ways:
$P=I^2R \\ P= \frac{V^2}{R}$
So for P=75W, we can use either of these to get R.  Let's use the first one:
$75W=(0.5A)^2R \\ \frac{75W}{0.25A^2}=300 \Omega$