the question: find the inductance of a coil that must be placed in series with a lamp requiring 2A, 400W at unity power factor when he supply is 230V, 50Hz. what exactly is a coil? i have read up on it, sometimes people say that coil is a inductor and a resistor, some people also say its just a inductor. im confused. help pls. thanks.

Coil is a reference to the geometry of a wire wound around a cylindrical non-conducting structure. When you do this it creates a circuit component with the property of inductance. We call this an inductor. An "ideal" inductor would be fabricated from wire which had no DC resistance. At room temperature no such wire exists. An actual inductor is constructed with wire that has some DC resistance. This is usually modeled as an ideal inductor in series with a small resistor. At very high frequencies things are a bit different, but you need to get your arms around DC/low frequency behavior before you go there.

A coil and inductor are the same thing. To make an inductor you make a coil of wire, sometimes around a magnetic core sometime not. All coils of wire have resistance. In many cases, the resistance is small enough to ignore. Analysis of the circuit will tell you if you can. I think you might be able to solve this using P=I*V and XL=2*PI*f*L. Use the first equation to find the voltage at the lamp. Use the second to find L. I'm guessing they expect you to ignore the resistance of the coil for this problem.