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Background Information

MEXLE is a Multimodal Experimental and Learning platform, designed to support self-directed and hands-on learning in electrical engineering.
The MEXLE-board is designed as a “lab-in-a-box” system that comes with a corresponding app. Electrical circuits can be built and tested on the board, while the app provides the experimental tasks together with the required background information.
At the moment, the system requires an external signal generator and an external oscilloscope. In a future version, the board itself will generate the required signals, with all signal settings controlled via the app. The oscilloscope function will also be integrated into the app, making an external oscilloscope no longer necessary.

MEXLE-board - Overview




MEXLE electronic components





Handling of the MEXLE components





RC network
RC circuits are commonly used to implement timers and delay circuits. In such applications, a capacitor is charged and discharged through a resistor. Since the capacitor voltage does not change instantaneously but rises and falls over time, the component values can be used to determine how long it takes to reach a specific voltage level.This principle is used, for example, in power-on delay circuits and timer-based flashing circuits. In the following experiment, the charging and discharging behavior of a capacitor will be investigated.

Capacitors must be charged via an electrical source.

A capacitor charges the faster the smaller the series resistor $R$ is. During charging, the voltage $u_{\rm C}$ results from a differential equation as:
$$ u_{\rm C}({\rm t})=U\cdot ({\rm 1}-e^{-\frac{t}{\tau}}), {\rm with~~} \tau = R\cdot C $$
The constant $\tau$ is called the time constant. After this time, the capacitor is charged to approx. ${\rm 63}~{\rm\%}$. The fundamental equation for the relation between current and voltage at a capacitor is:
$$ i_{\rm C}({\rm t})=C\cdot \frac{{\rm d}u_{\rm C}}{{\rm dt}} $$
From the two equations, the current through the capacitor is: $$ i_{\rm C}({\rm t})=\frac{U}{R}\cdot e^{-\frac{t}{\tau}} $$
The graphical representation of voltage and current during the charging of a capacitor over time is shown in figure 1.

Fig. 1: This is my little caption

Because of the exponential function, charging is theoretically only complete after an infinitely long time. The capacitor voltage equals ${\rm 63}~{\rm\%~} U$ after ${\rm 1}\cdot \tau$, ${\rm 86}~{\rm\%~} U$ after ${\rm 2}\cdot \tau$, ${\rm 95}~{\rm\%~} U$ after ${\rm 3}\cdot \tau$, ${\rm 98}~{\rm\%~} U$ after ${\rm 4}\cdot \tau$, and ${\rm 99}~{\rm\%~} U$ after ${\rm 5}\cdot \tau$. It is assumed that the capacitor is fully charged after a time span $T = {\rm 5}\cdot \tau$ and the voltage across the capacitor has reached $U$.

If the charged capacitor $C$ is discharged through a resistor $R$, the solution of the differential equation for the voltage is:

$$ u_{\rm C}({\rm t})=U\cdot e^{-\frac{t}{\tau}} $$
For the current accordingly:

$$ i_{\rm C}({\rm t})=- \frac{U}{R}\cdot e^{-\frac{t}{\tau}} $$

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