Final answer:
In a series circuit, two light bulbs with different resistances dissipate equal power because they have the same current flowing through them, even though their resistances are not the same.
Step-by-step explanation:
When two light bulbs with different resistances are connected in series and then connected across a battery, the true statement is that the power dissipated by bulb 1, which has greater resistance, is equal to the power dissipated by bulb 2, which has less resistance. This is because, in a series circuit, the current through both bulbs is the same. The power dissipated in a resistor is given by the formula P = I²R, where P is power, I is current, and R is resistance. As both light bulbs are connected in series, they will have identical currents flowing through them; thus the power dissipation is equal for both, despite the differing resistances.