One bulb lights brighter than the other of the two. Which bulb—when connected separately to the same voltage source rather than simultaneously—has the greater resistance?

Power: Power is the measure of how quickly an electric current does work. P stands for it. The watt is the SI unit of power (W).

Power dissipation comes from:

Power $\left(P\right)=VI=V^2/R=I^{2}R$

I have current running through me, yet there is resistance; where is the potential difference across resistance?

According to Ohm's law:

$V=IR$

Where V= Voltage, I= current flowing through the circuit, R= Resistance

Power $P=\frac{V^2}{R}$

The power is inversely proportional to the resistance according to the preceding formula, holding the potential constant.

Since the current is inversely proportional to resistance, the bulb that draws the most power will shine more than the others.

As a result, the dim bulb will have more resistance, whereas the brighter bulb will have lower resistance. Therefore, choice 4 is right.