Day 13 - Capacitors and Inductors

Topics Discussed

On day 13 of the ENGR 44 course, we were introduced to the basics of capacitors and inductors. We discussed the fundamental workings of capacitors first, noting that they work as a short before being charged and an open after being charged. We also viewed what happens when a capacitor is not aligned correctly relative to the direction of current flowing through it. (Video 1) No one wants to lose their fingers, so this demonstration was both important and entertaining, so we did it twice. We discussed how resistors must accommodate capacitors to prevent sparks from happening in circuits, and we did some example problems that involved capacitors (Fig. 1 & Fig. 2)

Fig. 1

Fig. 2

Additionally, we discussed inductors and how they work. We also discussed how we could treat them oppositely when compared to capacitors. We performed several practice problems with circuits involving inductors as well. (Fig. 3)

Fig. 3

Capacitor Voltage-Current Relations Lab

The first lab we performed in class focused on integrating a capacitor into a circuit and observing how it effected current and voltage within the circuit. We planned to use sinusoidal and triangular wave voltage inputs and see how the voltage across the capacitor would react. We predicted the shape of the resulting voltage that would occur across the capacitor given our newly acquired knowledge of how capacitors behave under such conditions. (Fig. 4) 

Fig. 4

Once we had this general idea, we created the circuit. (Fig. 5) Upon creating the circuit, we applied two separate sinusoidal waves, one with a 1k Hz frequency and the other with a 2k Hz frequency, both at an amplitude of 2V and offset of 0V. We also put in a triangular input voltage of 100 Hz frequency, 4V amplitude, and 0V offset. 

Fig. 5

In the measuring oscilloscope window, we got a reading for the input voltage and capacitor voltage. Additionally, we used the math channel to calculate the corresponding current going through the capacitor. Fig. 6 & 7 show our acquired graphs.

Fig. 6 - 1kHz Sine Wave

Fig. 7 - 2kHz Sine Wave

Inductor Voltage-Current Relations

For the second lab conducted in class, we used the exact same circuit created in the first lab, only this time instead of using a capacitor we used an inductor. Our measurements would all work the same way, that is in using the math channel on the oscilloscope to again calculate the current through the inductor using the measured voltage. We first created the circuit. (Fig. 8)

Fig. 8

We input the exact same sinusoidal waves and triangular waves into the inductor circuit, and we yielded the voltage and current that corresponded through the inductor itself. (Fig. 9, Fig. 10, & Fig. 11)

Fig. 9 - 1kHz Sine Wave

Fig. 10 - 2kHz Sine Wave

Fig. 11 - 100Hz Triangular Wave

Summary 

Upon completion of the labs, we were able to verify the predicted and derived relationships of capacitors and inductors to current and voltage respectively. Although not perfect, our results gave us information that was good enough to give us aggreement between theory and actual practice. These basic circuits and demonstrations will allow us to properly utilize these elements in future circuits. Additionally, we were introduced to the math channel in the oscilloscope window of our analog discovery device. This is a powerful tool, in that it allows us to construct real time graphs for several other circuit readings that could be obtained from measuring only a select few parts of the circuit.