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Basic Laws

Basic Laws. Instructor: Chia-Ming Tsai Electronics Engineering National Chiao Tung University Hsinchu, Taiwan, R.O.C. Contents. Ohm’s Law (resistors) Nodes, Branches, and Loops Kirchhoff’s Laws Series Resistors and Voltage Division Parallel Resistors and Current Division

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Basic Laws

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  1. Basic Laws Instructor: Chia-Ming Tsai Electronics Engineering National Chiao Tung University Hsinchu, Taiwan, R.O.C.

  2. Contents • Ohm’s Law (resistors) • Nodes, Branches, and Loops • Kirchhoff’s Laws • Series Resistors and Voltage Division • Parallel Resistors and Current Division • Wye-Delta Transformations • Applications

  3. Cross-section area A i + _ Meterial resistivity  v R Ohm’s Law • Resistance R is represented by 1  = 1 V/A ohm

  4. + _ i + _ i = 0 v = 0 v R =  R = 0 Resistors Short circuit Open circuit Variable resistor Potentiometer (pot)

  5. v Slope = R Slope = R(i) or R(v) i i Nonlinear Resistors Linear resistor Nonlinear resistor • Examples: lightbulb, diodes • All resistors exhibit nonlinear behavior. v

  6. 1 S = 1 = 1 A/V  mho siemens Conductance and Power Dissipation • Conductance G is represented by A positiveR results in power absorption. A negativeR results in power generation.

  7. a b + + _ _ c a b c Nodes, Branches, & Loops • Brach: a single element (R, C, L, v, i) • Node: a point of connection between braches (a, b, c) • Loop: a closed path in a circuit (abca, bcb, etc) • A independent loop contains at least one branch which is not included in other indep. loops. • Independent loops result in independent sets of equations. redrawn

  8. Continued + _ 5 2A 10V 2 3 Elements in series Elements in parallel • Elements in series • (10V, 5) • Elements in parallel • (2, 3, 2A) • Neither • ((5/10V), (2/3/2A))

  9. Kirchhoff’s Laws • Introduced in 1847 by German physicist G. R. Kirchhoff (1824-1887). • Combined with Ohm’s law, we have a powerful set of tools for analyzing circuits. • Two laws included, Kirchhoff’s current law (KCL) and Kirchhoff’s votage law (KVL)

  10. i1 i2 in Kirchhoff’s Current Law (KCL) • Assumptions • The law of conservation of charge • The algebraic sum of charges within a system cannot change. • Statement • The algebraic sum of currents entering a node (or a closed boundary) is zero.

  11. Proof of KCL

  12. i5 i1 i4 i2 i3 Example 1

  13. IT I1 I2 I3 IT Example 2

  14. Case with A Closed Boundary Treat the surface as a node

  15. _ _ _ v1 v2 vm + + + Kirchhoff’s Voltage Law (KVL) • Statement • The algebraic sum of all voltages around a closed path (or loop) is zero.

  16. + + _ _ v2 v3 _ _ + + v1 v4 v5 _ + Example 1 Sum of voltage drops = Sum of voltage rises

  17. a + V1 + + + + _ _ _ _ Vab V2 a + V3 _ Vab b _ b Example 2

  18. Example 3 2 v1 _ + _ v2 + 3 20V _ i + Q: Find v1 and v2. Sol:

  19. Example 4 + + v2 v3 _ _ 8 i1 i3 a _ v1 + i2 + 6 3 30V _ Loop 1 Loop 2 b Q: Find currents and voltages. Sol:

  20. R1 R2 i a Req i a _ _ _ + v1 v2 v + + + v _ + v _ b b Series Resistors

  21. R1 R2 i a Req i a _ _ _ + v1 v2 v + + + v _ + v _ b b Voltage Division

  22. Req R1 R2 RN i a i a _ _ _ _ v1 v2 v vN + + + + + v _ + v _ b b Continued

  23. i a i1 i2 R1 + R2 v _ b i a v Req or Geq + v _ b Parallel Resistors

  24. i a i1 i2 R1 + R2 v _ b i a v Req or Geq + v _ b Current Division

  25. i i a a i1 i2 iN R1 v + Req or Geq R2 RN + v v _ _ b b Continued

  26. i R1 R2 RN i a a _ _ i1 i2 iN v1 v2 _ + + vN + + _ + R1 v R2 RN v _ b b Brief Summary

  27. 4 1 2 Req 5 6 3 8 4 4 2 Req 6 Req Req 2 14.4 2.4 8 8 Example

  28. R1 R2 R3 R4 + _ vS R6 R5 How to solve the bridge network? • Resistors are neither in series nor in parallel. • Can be simplified by using 3-terminal equivalent networks.

  29. R1 R2 1 3 1 3 R1 R2 R3 R3 2 4 2 4 Rc Rc 1 3 1 3 Ra Rb Rb Ra 2 4 2 4 Wye (Y)-Delta () Transformations Y T  

  30. 1 3 R1 R2  R3 2 4 Rc 1 3 Rb Ra Y 2 4  to Y Conversion

  31. Y- Transformations

  32. a a 10 12.5 12.5 5 17.5 Rab Rab 30 70 30 35 20 15 15 b b a a 7.292 Rab Rab 9.632 21 10.5 b b Example

  33. Applications: Lighting Systems

  34. Applications: DC Meters Parameters: IFS and Rm

  35. Continued

  36. Continued

  37. Voltmeters Single-range Multiple-range

  38. Ammeters Single-range Multiple-range

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