Impedance and AC Analysis I Lab

In this lab we studied how a real inductor model needs a resistor in series to react to the resistance shown within the inductor.

Radial inductor used for this experiment

The impedance expresion of such combination looks like:

ZL, real = RL + jwL

The magnitude of the impedance relates also to the Voltage and Current phasors, |Vin| and |Iin|.

Step 1.
We measured the resistance of the unknown inductor to be
RL = 8.4 ohms

Step 2. Before proceeding to using the oscilloscope and the function generator, we first constructed the following circuit. Overwhelming current could potentially harm the equipment.

Because the function generator has a considerably high resistance, we also needed a DMM to measure voltage. In the picture above, Rext is to be valued at 68ohms.

Rext, actual = 71.3 ohm.

Once having done this, we set up the circuit and ran the frequency to be at 1Khz instead of 20khz.

We compared the voltages from the function generator and the Vrms voltage of the DMM to be at around 5 Volts each.

VIn, rms = 4.97V                         IIn, rms = 4.4 mA

As expected, there was a minor difference between the voltage readings from both devices because there are more operating components in the function generator.

Calculating the magnitude of the impedance  using the values above gives us

Z = V/I = 435.97ohms

Rewriting the expresion as a complex number gives us
Z  = Sqrt(R^2 + jwL) or,
435.97 = sqrt(5083.69 + jwL)

The angular frequency at which the circuit was being tested was
w = 125.669 rads/s

Having w, we can now solve for the value of L
L = 12.118mH

Step 3.
For this case we look at the following circuit which now contains a capacitor;

With this in mind and running at the same frequency of 1Khz, we want to set both the inductor and capacitor equal to each other

jwL = 1/jwC;           Using the value of L, we get the value of the capacitor to be:

C = 0.00218 mcFarads

We got the following reading in the oscilloscope:

The following readings were reported:
Vpp Ch1 = 10V
Vpp Ch2 = 5V
Delta t = 3mcseconds

We then used the DMM to obtain the following data:

Freq (Khz)	Vin (V)	Iin (mA)	|Zin| Ohms
5.00	5.66	0.67	8.45
10.00	5.29	1.60	3.31
20.00	4.90	2.14	2.29
30.00	5.49	1.10	3.66
50.00	7.43	1.72	4.32