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

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

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

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

7. Nodes, Branches, & Loops a c b Brach: a single element (R, C, L, v, i)+ _ a c b
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 + _ c b a

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

9. Kirchhoff’s Laws
Introduced in 1847 by German physicist G. R. Kirchhoff ( ).
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. 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. i1 i2 in

11. Proof of KCL

12. Example 1 i1 i3 i2 i4 i5

13. Example 2 IT I1 I2 I3 IT

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

29. Wye (Y)-Delta () Transformations1 2 3 4 R3 R1 R2 3 4 1 2 Y T Rb Rc 1 2 3 4 Ra Rb Rc 1 2 3 4 Ra  

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

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

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