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Series and Parallel Resistors

Series and Parallel Resistors. Objective of Lecture. Explain mathematically how resistors in series are combined and their equivalent resistance. Chapter 2.5 Explain mathematically how resistors in parallel are combined and their equivalent resistance. Chapter 2.6

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Series and Parallel Resistors

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  1. Series and Parallel Resistors

  2. Objective of Lecture • Explain mathematically how resistors in series are combined and their equivalent resistance. • Chapter 2.5 • Explain mathematically how resistors in parallel are combined and their equivalent resistance. • Chapter 2.6 • Rewrite the equations for conductances.

  3. Series Resistors

  4. Series Resistors (con’t) • Use KVL

  5. Series Resistors (con’t) • Use KVL • Use Ohm’s Law

  6. Series Resistors (con’t) • Use KVL • Use Ohm’s Law • Substitute into KVL equation

  7. Equivalent Resistance: Series Connections Req is equal to the sum of the resistors in series. In this case: Req = R1 + R2

  8. General Equations: Series Resistors • If S resistors are in series, then where Vin may be the applied voltage or the total voltage dropped across all of the resistors in series.

  9. Parallel Resistors

  10. Parallel Resistor (con’t) • Use KCL

  11. Parallel Resistor (con’t) • Use KCL • Use Ohm’s Law

  12. Parallel Resistor (con’t) • Use KCL • Use Ohm’s Law • Substitute into KCL equation

  13. Equivalent Resistance: Parallel Connections 1/Req is equal to the sum of the inverse of each of the resistors in parallel. In this case: 1/Req = 1/R1 + 1/R2 Simplifying (only for 2 resistors in parallel) Req = R1R2 /(R1 + R2)

  14. General Equations: Parallel Resistors • If P resistors are in parallel, then where Iin may be the total current flowing into and out of the nodes shared by the parallel resistors.

  15. If you used G instead of R • In series: The reciprocal of the equivalent conductance is equal to the sum of the reciprocal of each of the conductors in series In this example 1/Geq = 1/G1 + 1/G2 Simplifying (only for 2 conductors in series) Geq = G1G2 /(G1 + G2)

  16. If you used G instead of R • In parallel: The equivalent conductance is equal to the sum of all of the conductors in parallel In this example: Geq = G1 + G2

  17. Electronic Response:For the same value resistors As you increase the number of resistors in series Does Req increases or decreases? As you increase the number of resistors in parallel Does Req increases or decreases?

  18. Summary • The equivalent resistance and conductance of resistors in series are: where S is the total number of resistors in series. • The equivalent resistance and conductance of resistors in parallel are: where P is the total number of resistors in parallel.

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