I have had a few people ask me over the years if their transformer is bad because they do not measure the rated resistance of the transformer. Transformers and other coils have two measurements of ohms: The AC resistance (impedance) and the DC resistance.
When looking at an electrical circuit or coil, it acts one way to DC (direct current) then AC (alternating current). Capacitance and frequency does not have an effect with DC. To DC in a circuit all capacitors are open. This means that DC voltage cannot flow through them, and all that is measured is the resistance. In a coil, like a transformer or speaker, the resistance of the wire is measured. Most multi-meters only measure DC resistance. They inject a DC voltage to measure it.
AC voltage is an alternating voltage. The speed of the alternating cycle is the frequency. To measure AC you need to inject an AC voltage at a specific frequency. Because of the voltage alternates, capacitance plays a major roll. Circuits that have capacitors in combination with resistors and other devices, allow AC to pass current through. The reactance of the circuit will change with the change of frequency. In a coil, you have a capacitance between winding and the DC resistance of the wire. This is what determines the AC resistance of the coil. When you read a spec of a coil, like a speaker or audio transformer, you get an ohm rating at a specific frequency. They are typically rated at 1,000 Hz. When you see a speaker that is rated at 8 ohms, that means that the AC resistance is 8 ohms at 1,000 Hz.
There are many formulas for calculating the AC resistance of circuits and coils. The formulas would take up pages and need explanations for each. There are many handbooks of electronic formulas on the market today. If you are more interested in impedance, you may wish to take a look.
