Impedance and AC Analysis I

The purpose of this lab is to analyze and study a real inductor.

Procedure:
We start with a real inductor connected in series with an external resistance.
2 Multimeters are taking measurements.

We measured R_L = 8.3 Ω
R_ext = 67.2 Ω
We measure our V_rms = 5V at 1000 Hz.

The built circuit

V_in,rms = 4.93 V
I_in,rms = 65.0 mA 
The voltage reading differs from the FG because internal resistane drop 0.7 V
V_in/I_in = Z_L = 75.8 Ω
Z_L = sqrt((R_ext + R_L)^2 + (ωL)^2)
ω = 6280 rad/s
L = 1.16 mH

Adding a capacitor to cancel inductance impedance
1/ωC = ωL
C = 1/(ω^2*L) = 2.19 *10^-5 F

Remodified circuit

V_pp, CH1 = 1.5V
V_pp, CH2 = 20mV
deltaT = 0.4 ms
Phase difference = (deltaT) *6240* 360 ° = 184.32 °

Analysis:

Frequency (kHz)	V_in (V)	I_in (A)	|Z_in| (Ω)
5	4.6	0.073	63.0137
10	4.2	0.0719	58.41446
20	3.51	0.0691	50.79595
30	3.51	0.0653	53.75191
50	4.5	0.0558	80.64516

Questions:
1. It is not the largest at 20 kHz as we used 1 kHz for calculations. Largest current should be at 1 kHz as imaginary part cancels out.

2. V_L = Z_L/Z*V_in
V_L = 2.8574 +  1.2737i
Phasor = 24.0243 °

3. The circuit looks more inductive as imaginary part is always positive.

4. The circuit looks more inductive as imaginary part is always positive.

Conclusion:
The experiment was successful; however, the answers to the questions may not be as expected as it assumes the capacitor was calculated at 20 kHz instead of 1 kHz.