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Lecture 5

Lecture 5. Review: Series, parallel circuit elements Circuit reduction Related educational modules: Section 1.5. Review: series and parallel circuit elements. Elements in series if they have the same current Elements in parallel have the same voltage. Circuit reduction.

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Lecture 5

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  1. Lecture 5 Review: Series, parallel circuit elements Circuit reduction Related educational modules: Section 1.5

  2. Review: series and parallel circuit elements • Elements in series if they have the same current • Elements in parallel have the same voltage

  3. Circuit reduction • Some circuit problems can be simplified by combining elements to reduce the number of elements • Reducing the number of elements reduces the number of unknowns and thus the number of equations which must be written to determine these unknowns

  4. Series circuit elements – example 1 • Apply KCL at any node  all elements have the same current • All of the above circuit elements are in series

  5. Series element circuit reduction – example 1 • KVL around the loop: -V1 + i·R1 + V2 + i·R2 + i·R3 – V3 + i·R4 = 0 (-V1 + V2– V3) + i(R1 + R2 + R3 + R4) = 0

  6. Series circuit reduction • Notes: • Voltage sources in series add directly to form an equivalent voltage source • Resistances in series add directly to form an equivalent resistance

  7. Series circuit reduction – Example 2 • Determine the power delivered by the 20V source

  8. Voltage Division • Series combination of N resistors:

  9. Voltage Divider Formula • Ratio of VK to the total voltage is the same as the ratio of RK to the total series resistance

  10. Voltage Dividers – special case • Voltage source in series with two resistors:

  11. Voltage division – example 1 • Determine the power dissipated by the 2 resistor

  12. Voltage division – example 2 • Determine the voltage V1 in the circuit below.

  13. Parallel circuit elements – example 1 • Apply KVL around any loop  all elements have the same voltage • All of the above circuit elements are in parallel

  14. Parallel element circuit reduction – example 1 • KCL at upper node:

  15. Parallel circuit reduction • Notes: • Current sources in parallel add directly to form an equivalent current source • Definition: Conductance is the inverse of resistance • Units are siemens or mhos (abbreviated S or ) • Conductances in parallel add directly to form an equivalent conductance

  16. Go back to previous example, look at it in terms of conductances

  17. Parallel element circuit example 1 – revisted

  18. Parallel circuit reduction – Example 2 • Determine the power delivered by the 2A source

  19. Current Division • Parallel combination of N resistors:

  20. Current Divider Formula • Ratio of iK to the total current is the same as the ratio of GK to the total parallel conductance

  21. Current Divider – special case • Current source in parallel with two resistors

  22. Current division – example 1 • Determine the current in the 2 resistor

  23. Current division – example 2 • Determine the value of R which makes i = 2mA

  24. Circuit Reduction • Series and parallel combinations of circuit elements can be combined into a “equivalent” elements • The resulting simplified circuit can often be analyzed more easily than the original circuit

  25. Circuit Reduction – example 1 • Determine the current in the 2 resistor. (Note: we wrote the governing equations for this example in lecture 3.)

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