The internal resistance of a non-ideal inductor in an RLC series circuit at resonance

The measured voltage at the inductor in an RLC series circuit connected to a sinusoidal electromotive force depends on the current and the impedance. The latter does not only include the inductive reactance only but also the ohmic resistance of the inductor. This fact has a clear consequence on the result of the measurement as the measured voltage at the inductor is not in counterphase with the measured voltage at the capacitance as shown in theory where ideal inductors are usually considered. In this work, the resistance of a coil in an RLC circuit is obtained from the direct measurements of the phase of the voltage at the coil at resonance and the resonant frequency for different values of capacitance. This value is compared with the resistance of the coil determined directly with an ohmmeter. The agreement between both values is very good. The conventional signal generator has been replaced by a smartphone which is a very familiar device for the students. The smartphone can provide the necessary voltage supply for the experiment to be carried out successfully.