Impedance and AC Analysis

PROBLEM
We model a "real" inductor. We must include a series resistance to account for the resistance of the many turns of wire in the inductor. The impedance looking into a real inductor: Zreal = R + jwL

METHOD
We measure the inductor's "unknown" resistance with an ohmmeter. R = 7.8 ohms

We set Rext = 68 ohms, measure and record your mounted resistor. Rext(actual) = 68.5 ohms

Energize the FG. Set the frequency to be 20kHz sinusoid. Set RMS to be 5.00. Connect a DMM to the output of the FG and ensure you have 5.00 Vrms out of the FG.

Next we construct a circuit similar to the figure.
Using a DMM, measure Vin and I in.
Vin(rms) =  5.23 V
I in(rms) = 22.11 mA

Calculate the magnitude of the impedance using the voltage and current from above.
Z=V/i = 236.5 ohms

Rewrite input impedance as a complex number: R + jwL = 7.8 + 279j ohms
|Z| = 279 ohms

What is the angular frequency at which the circuit is operating?   w = 40*pi Krad/s


7.8 + 40piKL = 236.5 >> L = 1.82 mH
Consider the circuit below. Suppose our source is set to 20kHz. We wish the capacitor to cancel the inductive part of the real inductor. Calculate the value of the capacitance.
This occurs at resonance >> wL=1/wC >> C=1/(L*w^2) >> C = 28nF

Energize the scope. Connect CH1 Across the DMM. Connect CH2 to the top of the real inductor. Adjust the scope to see both waveforms. Take scope measurements at 20kHz.

Vpeak2peak(CH1) = 10 V
Vpeak2peak(CH2) = 24 V
dt = 14.5 us

phase_difference = Tx(f)(360) = 94 degrees

DATA

Frequency	Vin (V)	I in(A)	|Z in| (ohms)
5 kHz	5.78	7.1	0.814
10 kHz	5.41	20.1	0.269
20 kHz	5.03	60.1	0.084
30 kHz	5.88	0.00	Infinite
50 kHz	8.24	0.00	Infinite