In this experienment we built an RC circuit on a breadboard, and subsequently subject the electrical system to a step input in the form of changing the input pin's signal from "high" to "low". After observing the experimental signal on an oscilloscope, we used ADC to record the voltage output and then sent the data to our PC via serial communication for plotting in our IDE of choice. We subsequently determined the RC circuit's experimental and theoretical time constants and compared them. Figure 1 displays a plot of our experimental voltage versus time data. The first order response to the step input is apparent by inspection.
Figure 1. RC circuit response to step input; R = 51 kΩ, C = 3.3 μF.
With a resistance value of 51 kΩ and a capacitance of 3.3 μF, the theoretical time constant is ~0.17 seconds. By crude inspection of Figure 1, we see that it takes ~180-190 ms to reach 63.2% of the steady state value. Figure 2 displays an annotated plot of RC voltage versus time.
Figure 1. Annotated RC circuit step response; R = 51 kΩ, C = 3.3 μF.
The experimental and theoretical time constants closely match, with a percent error of 5-10%.