How much power will be dissipated by a 12 ohm resistor if 6 volts are applied across it?

A 12 ohm resistor with 6 volts across it will dissipate 3 watts of power.

Current = voltage divided by resistance = 6 / 12 = 0.5 amperes.

Power = voltage times current = 6 * 0.5 = 3 watts.