Superposition theorem is a key principle in circuit analysis, allowing for the simplification of complex circuits into manageable parts. This theorem states that in a linear circuit with multiple sources, the voltage across (or current through) an element can be determined by considering each source independently and then summing the effects. This experiment focuses on applying superposition to understand how resistors behave in a circuit with multiple voltage sources.

**Materials and Setup**

- Red Pitaya or equivalent device capable of providing 5V, 3.3V, and GND outputs.
- Resistors of known values to construct the circuit.
- Oscilloscope with at least two channels, set up to measure DC voltages.

**Superposition Theorem Application**

**Total Voltage across a Resistor in a Multi-Source Circuit**- The voltage across any resistor in a circuit containing multiple voltage sources can be considered as the sum of the voltages across that resistor due to each source acting alone.
- When considering one source at a time, all other voltage sources are replaced by their internal resistance, typically resulting in a short circuit for ideal voltage sources.
**Voltage Division Rule**- When a source is considered active, the voltage drop across any resistor in series can be determined by the voltage division rule: $V_{R_x}=V_s \cdot (\frac{R_x}{R_{total}})$
- Where
*V**s*is the source voltage,*R**x*is the resistor of interest, and*R**t**o**t**a**l*is the sum of resistances in the series path.

**Experiment**

**Experiment**

There is always an experiment. But this one will be extra simple. Build a circuit and learn how to efficiently measure it. 5V, 3.3V, and GND are stolen from the Red Pitaya and both probes are set to 10x mode.

Since this is a DC circuit with no AC stimulation, channels 1 and 2 will be just straight lines, effectively acting as voltage meters. Voltage drop between nodes can be automatically calculated by selecting MATH->Operator = â€śminusâ€ś->ENABLE. It would also be wise to add automatic measurements on all signals by clicking MEAS->Operator = â€śMEANâ€ť ->DONE. Do this for all signals, IN1, IN2, and MATH. You can now play around with analyzing this circuit. Or maybe you would like to build a fancier one and play around with it. Red Pitaya has one more voltage output pin, -4V, hint hintâ€¦

**Exploration and Analysis**

**Superposition Principle:**Through direct measurement, explore how the superposition theorem applies to your circuit. Analyze how each power source independently affects the voltage across each resistor, and then observe the cumulative effect.**Circuit Modifications:**Consider incorporating the Red Pitayaâ€™s -4V output to introduce another voltage source into the circuit, further complicating the network and allowing for a deeper exploration of superposition.

**Conclusion**

This straightforward experiment offers a hands-on approach to understanding the superposition theorem and its practical applications in circuit analysis. By constructing a simple resistor network and utilizing the Red Pitayaâ€™s multiple voltage outputs, participants gain insight into the fundamental principles governing current flow and voltage distribution in electrical circuits. This exercise not only reinforces theoretical knowledge but also enhances skills in circuit construction, measurement, and analysis, serving as a foundation for more complex investigations in the future.