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Solving a Series Circuit with Multiple Resistors

This text explains how to calculate currents and voltages in a series circuit with multiple resistors using Ohm's law.

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Solving a Series Circuit with Multiple Resistors

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  1. 3Ω 17 V A3 V3

  2. A4 A1 V4 V3 V1 A3 A2 V2 9Ω 6Ω 10Ω 12Ω 8Ω 37 V 7Ω 11Ω 13Ω

  3. 9Ω A2 V4 A1 6Ω 10Ω 12Ω V2 8Ω 37 V A3 V1 V3 7Ω 11Ω A4 13Ω

  4. 9Ω A2 V4 A1 6Ω 5.4545Ω 8Ω 37 V V1 V3 7Ω 11Ω A4 13Ω

  5. 9Ω A2 V4 A1 6Ω 5.4545Ω 8Ω 37 V V1 V3 7Ω 11Ω A4 13Ω

  6. 9Ω A2 V4 A1 6Ω 5.4545Ω 8Ω 37 V V1 V3 7Ω 5.9583Ω

  7. 9Ω A2 V4 A1 6Ω 5.4545Ω 8Ω 37 V V1 V3 7Ω 5.9583Ω

  8. A2 A1 6Ω 20.4129Ω 8Ω 37 V V3 7Ω

  9. A2 A1 6Ω 20.4129Ω 8Ω 37 V V3 7Ω

  10. Finally we have a simple series circuit: A2 6Ω 5.7475Ω 37 V V3 7Ω

  11. Solving: Rtot = 6 + 7 + 5.7475 = 18.7475Ω I = V/R = 37/18.7475 = 1.9736 A So A2 reads 1.9736 A and V3, the voltage across the subcircuit = IR = 1.9736*5.7475 = 11.3432 V We will use this voltage to solve the rest of the subcircuit… A2 6Ω 5.7475Ω 37 V V3 7Ω

  12. Solving the subcircuit: The current through the 8Ω is just V/R = 11.3432/8 = 1.4179A which is the reading on A1 A1 20.4129Ω 8Ω 11.3432 V

  13. Now we have: 20.4129Ω 11.3432 V

  14. Which is really 9Ω V4 10Ω 12Ω V2 11.3432 V A3 V1 11Ω A4 13Ω

  15. But let’s go back to: 9Ω V4 V2 5.4545Ω 11.3432 V V1 5.9583Ω

  16. Solving: Rtot = 9 + 5.4545 + 5.9583 = 20.4129Ω And I = V/R = 11.3432/20.4129 = .5557 A Using IR to pick off the voltages: V4 = .5557*9 = 5.0012 V V2 = .5557*5.4545 = 3.0310 V V1 = .5557*5.9583 = 3.3110 V These are also the voltages across the remaining subcircuits. 9Ω V4 V2 5.4545Ω 11.3432 V V1 5.9583Ω

  17. The first sub circuit: 3.0310 V 5.4545Ω

  18. Which is really: 3.0310 V 10Ω 12Ω A3

  19. The current through the 10Ω is just V/R = 3.0310/10 = .3031 A 3.0310 V 10Ω 12Ω A3

  20. The last sub circuit: 3.3110 V 5.9583Ω

  21. Which is really: 3.3110 V 11Ω 13Ω A4

  22. The current through the 13Ω is just V/R = 3.3110/13 = .2547 A 3.3110 V 11Ω 13Ω A4

  23. The current through the 13Ω is just V/R = 3.3110/13 = .2547 A Ta Daaa! 3.3110 V 11Ω 13Ω A4

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