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!
Best Answer
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 $R^2$.