380 likes | 585 Views
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
E N D
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 • Wye-Delta Transformations • Applications
Cross-section area A i + _ Meterial resistivity v R Ohm’s Law • Resistance R is represented by 1 = 1 V/A ohm
+ _ i + _ i = 0 v = 0 v R = R = 0 Resistors Short circuit Open circuit Variable resistor Potentiometer (pot)
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
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.
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
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))
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)
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.
i5 i1 i4 i2 i3 Example 1
IT I1 I2 I3 IT Example 2
Case with A Closed Boundary Treat the surface as a node
_ _ _ v1 v2 vm + + + Kirchhoff’s Voltage Law (KVL) • Statement • The algebraic sum of all voltages around a closed path (or loop) is zero.
+ + _ _ v2 v3 _ _ + + v1 v4 v5 _ + Example 1 Sum of voltage drops = Sum of voltage rises
a + V1 + + + + _ _ _ _ Vab V2 a + V3 _ Vab b _ b Example 2
Example 3 2 v1 _ + _ v2 + 3 20V _ i + Q: Find v1 and v2. Sol:
Example 4 + + v2 v3 _ _ 8 i1 i3 a _ v1 + i2 + 6 3 30V _ Loop 1 Loop 2 b Q: Find currents and voltages. Sol:
R1 R2 i a Req i a _ _ _ + v1 v2 v + + + v _ + v _ b b Series Resistors
R1 R2 i a Req i a _ _ _ + v1 v2 v + + + v _ + v _ b b Voltage Division
Req R1 R2 RN i a i a _ _ _ _ v1 v2 v vN + + + + + v _ + v _ b b Continued
i a i1 i2 R1 + R2 v _ b i a v Req or Geq + v _ b Parallel Resistors
i a i1 i2 R1 + R2 v _ b i a v Req or Geq + v _ b Current Division
i i a a i1 i2 iN R1 v + Req or Geq R2 RN + v v _ _ b b Continued
i R1 R2 RN i a a _ _ i1 i2 iN v1 v2 _ + + vN + + _ + R1 v R2 RN v _ b b Brief Summary
4 1 2 Req 5 6 3 8 4 4 2 Req 6 Req Req 2 14.4 2.4 8 8 Example
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.
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
1 3 R1 R2 R3 2 4 Rc 1 3 Rb Ra Y 2 4 to Y Conversion
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
Applications: DC Meters Parameters: IFS and Rm
Voltmeters Single-range Multiple-range
Ammeters Single-range Multiple-range