Explain how an ohmmeter can measure the resistance of a component (such as a light bulb) when there is no battery or other source of power connected to it.

Ohmmeters always carry an internal source of electrical power (usually a battery). The component under test can be tested by supplying it with a small amount of current, in order to measure its resistance to that given current.

If the component were open circiuted, the ohmmeter would register an extremely large (infinite) amount of resistance. Also measuring the resistance of a powered device will give an ernomously wrong value of resistance (if it doesn't burn the ohmmeter first)