Nodal Analysis

Objective: we wish to make a circuit that can still power two loads while obtaining damage from the dangerous world around us.

Circuit Chosen:

Note: this circuit contains multiple batteries which helps to satisfy our objective of damage proofing our circuit. If one battery fails we have one more.

Step 1A: Nodal Equations

Boring Math: (Unless you are into that kind of thing)

Step 1B: VB=V2, VC=V3

Currents:

Note the currents above are shown to be negative due to the orientation given to them in the diagram; however, they would be taken to be positive leaving the battery. 

Show me the POWER: of each battery

Step 3: Chart of nomial and measured values as well as power ratings of each component in circuit.

Note the measured values reasonably resemble the nominal values which would imply lower margins of error when doing final calculations.

Step 5: lets do it

Actual Circuit

Data

Conclusion: the margins of error are larger then i would have expected. If time was unlimited i would have liked to redo the experiment to make sure the circuit was built correctly or other errors were not made. 

Step 6:

Pbat1 = (10.71V)(13.4mA) = 0.144W

Pbat2 = (2.4mA)(10.9V) = 0.0242W

Now we are V2=V3=9V

Circuit Produced:

Measurements

 V2 = 9.05 V

V3 = 9.07 V

Ibat1 = 9.1 mA

Ibat2 = 8.9 mA

Conclusion: the two voltage readings are very close to 9 V makings me feel that we did something right.

The End