## Measuring RC Circuit Current with an Arduino

Published 2021/09/26 by Jordan Hay

Using the analog pins of an Arduino it is possible to measure the voltage across a resistor. With a known value of resistor this can be used to deduce the current flowing in a circuit* using ohm's law

\begin{align}\Delta V = IR\end{align}

With the ability of an Arduino to quickly and accurately sample the voltages analysis can be performed that far outstrips the ability of a human with a multimeter. To highlight this the following experiment was conducted in order to verify the equation describing the current in an Resistor and Capacitor (RC) circuit

\begin{align}I(t) = \frac{\varepsilon}{R}e^{-\frac{t}{RC}}\end{align}

Where $I(t)$ is the current as a function of time, $\varepsilon$ the voltage provided to the circuit, $R$ the resistance of the resistor in the circuit, and $C$ the capacitance of the capacitor. A general rule of thumb for RC circuits is that the capacitor will charge in 5 time units $\tau$ where

\begin{align}\tau = RC\end{align}

Given a capacitor of size $100\times 10^{-6} F$ and a resistor $220 \Omega$, the capacitor will reach capacity in roughly $0.11 s$. An almost unobservable amount of time for a human, however these were the components selected for the analysis.

The circuit and arduino was set up per Figure 1 with analog pins A0 and A1 connected either side of the resistor, and +5V and GND pins used to power the circuit. Figure 1 - Arduino setup with analog pins connected to either side of the resistor. Note the arduino was also used to supply 5V to the circuit.

The arduino was set to output the time (in $ms$), voltage before the resistor, and voltage after using the serial monitor. The relevant data was then processed with python and Figure 2 generated. Figure 2 - Graph with predicted and measured current of the circuit. The predicted model was made with Equation 2.

Surpsingly the data found and the model match up near perfectly, with the current dropping to near zero in roughly $100-150 ms$, as the rule of thumb predicted. The apparent lag behind the model could be due unideal component behaviour or inaccuracy in the data.

UPDATE (19/10/2021):

Code used to analyse data from Arduino is now avaliable on my Github.

*With >5V and a common ground.