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Resistor Voltage Divider

Quick Theory

Voltage, Current, and Resistance

Electric circuits are governed by basic principles where voltage is the electrical potential difference, current is the flow of electric charge, and resistance opposes current. Understanding these fundamentals is crucial for analyzing and constructing circuits.

Ohm's Law and Kirchhoff's Laws

Ohm's Law (V=IR) explains the relationship between voltage (V), current (I), and resistance (R), foundational for calculating voltage drops across resistors.

V=I\cdot R

Voltage Devider Rule: For two resistors $R_1$ and $R_2$ in series the voltage across $R_2$ is:

V_{out}=V_{in} \frac{R_2}{R_1+R_2}

Series Circuit Resistance:

R_{\text{total}} = R_1 + R_2 + \dots + R_n

Parallel Circuit Resistance:

\frac{1}{R_{\text{total}}} = \frac{1}{R_1} + \frac{1}{R_2} + \dots + \frac{1}{R_n}

Current Law (KCL) states that the total current entering a junction equals the total current leaving it.

\sum \text{I}_{\text{in}} = \sum \text{I}_{\text{out}}

Kirchhoff's Voltage Law (KVL) asserts that the sum of all voltages around a closed loop is zero, essential for analyzing circuits with multiple loops.

\sum V_{\text{loop}} = 0

Practical Application

Choosing Resistors: Start with resistors of at least 100 ohms to prevent damage, understanding the role of resistance in voltage and current control.
Building the Circuit: Follow detailed instructions to construct the voltage divider on a breadboard, highlighting the significance of each step in relation to Ohm's and Kirchhoff's laws.
Measuring and Calculating Voltages: Emphasize the process of measuring voltages across resistors, using the mean value for more accurate readings, and calculate expected voltages using the provided equations to reinforce theoretical knowledge.

In the context of circuit analysis, it is common to use equations to solve for voltage, current, and power. For this experiment, we will construct a circuit using Red Pitaya and measure the voltage across resistors to test our calculations.

To begin, select resistors with values of at least 100 ohms to avoid any potential damage. Once you have chosen your resistors, build the circuit on a breadboard according to the provided diagram.

Next, choose the voltage source for U_0 from Red Pitaya’s supply pins. You have the option to use 3.3 V, 5 V, or even -4 V depending on the requirements of your specific circuit.

After constructing the circuit and selecting the appropriate voltage source, connect probes in 10x mode to Red Pitaya and launch the oscilloscope application. Make sure to set the x10 attenuation in the software as well.

Since we are working with DC signals, it is not necessary to connect the alligator clips, as they are internally connected to Red Pitaya’s GND. You can measure the voltage on any node by connecting a probe to it.

To make reading voltage easier, you may want to set up automatic mean measurements on both channels. This can be done by navigating to the “MEAS” menu and selecting “Operator = MEAN” for each channel, then selecting “DONE.” This will display the average voltage for each channel, making it easier to read and interpret the measurements.

I recommend constructing a circuit with no more than three branching nodes to simplify the calculations. Select resistors and connect them in a suitable configuration. Next, use Ohm’s Law and Kirchhoff’s Laws to calculate the expected voltage drops in the circuit.

To verify the accuracy of the calculations, you can compare the calculated voltage drops with the measured values obtained by using probes connected to the circuit.

Written by Luka Pogačnik Edited by Andraž Pirc

This teaching material was created by Red Pitaya & Zavod 404 in the scope of the Smart4All innovation project.