Electric power

Power is a rate of energy transfer, and for a circuit element the rate depends on the current in the element and the potential difference across it:

That is the only power equation printed in the Electricity group of the AP Physics 2 sheet. The CED lists $P = I^2 R$ and $P = (\Delta V)^2 / R$ as derived equations: substitute $\Delta V = IR$ into the first form, or $I = \Delta V / R$ into it, and you have them. All three say the same thing, and the two derived forms need the element to be ohmic before $R$ means anything fixed.

Which form to reach for depends on what is being held constant.

• Current is the shared quantity through a series string, so use $P = I^2 R$ there. More resistance then means more power dissipated.
• Potential difference is the shared quantity across parallel branches, so use $P = (\Delta V)^2 / R$. More resistance then means less power.

Those conclusions are opposites, which is why "does the bigger resistor dissipate more power" can only be answered after asking how it is connected. Since the brightness of a bulb increases with its power, the same reasoning settles which bulb in a network glows brightest.

Energy is power times time: a 60 W bulb left on for 120 s converts 7200 J. The Ohm's law guide sets up the currents and voltages you feed in.