Day 18 Impedance

Today's lab concentrated on finding the observable impedance of three circuit elements, a resistor, inductor, and capacitor. Impedance is a circuit element's resistance to AC voltage, similar to the resistance of an element in DC. Impedance is much more efficient to work with because it there is no discrimination against the type of element: unlike the behavior of a capacitor or inductor to DC voltage.

The circuits were wired according to the diagrams shown below. The impedance for the three circuit element can be easily calculated with the use of known impedance formulas. The impedance of a resistor is just Z = R, so the impedance is really just the resistance of the resistor. For a capacitor, the impedance can be calculated as Z = 1/(jωC) , where j is the imaginary component, ω is the angular velocity of the input, and C is the capacitance of the capacitor. The impedance of an inductor is Z = jωL, where L is the inductance of the inductor. The phase angles for a resistor, capacitor, and inductor are 0°, -90°, and 90°, respectively.

Below is the pre lab for our experiment.

We connect a constant resistor R = 47 ohms in each of the circuits. We used the Oscilloscope from our analog discovery to represent the voltage across the resistor so that we can compare it to each of the changing circuit elements: the resistor, the inductor, and the capacitor.

Below is the resistor in series with a resistor circuit. For some reason, I did not take my own pictures of each of my circuits, so all photo credit to Clark on the circuit pictures.

I did, however, successfully measure and observe the different outputs of each of the circuits. Below is the output voltage across our second resistor at three different frequencies.

Those frequencies being:

1kHz, 5kHz, and 10kHz

As expected, we see two sinusoidal waveforms both in phase with each other. Reason being, the impedance of a resistor is in phase with the impedance of another resistor, both at phase angles 0°. The third function, M1, is a math function that shows the current that flows through the circuit. 

At a higher frequency, we still observe that the waves are still in phase, as shown in the screenshots above and below. 

This shows that the impedance of a resistor maintains a relatively constant characteristic regardless of frequency.

The next lab analyzed is the RL circuit displayed above.

We will follow the same procedures for the RL circuit and the RC circuit below.

In this circuit we see Channel C1, the output across the inductor, to be +90° out of phase with our resistor, precisely what we predicted in our pre-lab. As shown in the following screenshots, the frequency is negligible when considering the phase relationship between the inductor and the resistor.

The readings in the front window of the screen shot shows that the inductor still leads the resistor by 90°, as predicted.

Finally, the RC circuit will be analyzed below.

Below are the measured outputs across the capacitor:

Here we see the capacitor output, measured by Channel C2, lagging the resistor by -90°, once again stated in the pre-lab as expected. 

 AC impedance seems to be a lot less convoluted (once we review our complex numbers) than DC. It is a lot more simple being able to simplify different circuits down into equivalent impedances. While AC has been a pain in the past, this experience with it should flow with a little less impedance. Get it?