# Measuring inductance and resistance of a coil

If you had a resistive coil with an inductance and a resistance, a sinusoidal voltage source with a variable frequency, and a meter that can measure rms voltages and currents, how would you go about determining the inductance and resistance of the coil?

I know that the complex impedance of the coil is $$i\omega L + R$$, so the current through the coil will be $$I = \frac{V}{i\omega L + R}$$, but I am not sure what to do from this.

Any help would be appreciated!

Since $$\left (\dfrac{V_{\rm rms}}{I_{\rm rms}}\right )^2=L^2\, \omega^2+R^2 = (4\,\pi^2 L^2)\, f^2+R^2$$ is of the form of the general equation of a straight line, $$y = m\,x +c$$, then taking a series of $$V_{\rm rms}$$ and $$I_{\rm rms}$$ readings at different frequencies, $$f$$, and drawing a graph of $$\left (\dfrac{V_{\rm rms}}{I_{\rm rms}}\right )^2$$ against $$f^2$$ should give a straight line of gradient $$4\,\pi^2 L^2$$ and intercept on the $$\left (\dfrac{V_{\rm rms}}{I_{\rm rms}}\right )^2$$ axis of $$R^2$$.
With your meter you can measure only the rms of voltage and current, but not their phases. Therefore from the complex impedance $$\frac{V}{I}=Z=i\omega L+R$$ you can only measure its absolute value $$\frac{V_\text{rms}}{I_\text{rms}}=|Z|=\sqrt{(\omega L)^2+R^2}.$$
So with your meter you need to measure $$|Z|$$ for at least two frequencies (or for DC and one frequency). From these $$|Z|$$ values you can then calculate $$R$$ and $$L$$.