(4/18/17) Day 16: Passive RC and RL Circuit Natural Response

Lecture:

In lecture today, we focused on source free circuits containing capacitors and inductors.
First, we derived the voltage as a function of time.

Then we calculated a time constant that would help predict the amount of time a capacitor would take to completely charge and discharge.

We also calculated the frequency of a circuit from that using a pretty simple formula.

This problem was to test our techniques with inductors and their own time constant formulas/equivalency rules!

This is an exercise in using the time constant/inductor techniques to find a function of current on an inductor of time (t).

Lab 1

Passive RC Circuit Natural Response

This lab was intended to examine the natural response of an RC circuit when a voltage supply is abruptly disconnected.

The circuit originally looks like the left because the voltage is placed on it.

We are then going to simulate turning off the source by "pulling" the voltage source and observing the capacitors behavior.

Prelab:

To begin, my team and I were asked to calculate the time constant Tau = RC.

Live Trial:

Due to a failure to get acceptable measurements, I was forced to continue the experiment at home, 

I then fabricated the circuit in question on a breadboard, then used every circuit as a useful tool to determine the result of pulling the voltage source from the circuit.

Here is the circuit in every circuit software

And now here is the voltage source applied to it.

I then simulated the voltage source being pulled by using a switch and opening/closing the circuit while watching the voltmeter chart created over the capacitor.

I then zoomed in on a portion of the wave that was discharging, and got this chart.

The max voltage on the capacitor (the initial during the open switch) was 3.48V. Doing a percentage error calculation on it yields... 0.0575%. Pretty spot on.