Chapter 2 Basic Laws 基本定律 2.1 Ohm's Law 2.2 Kirchhoff's Laws 2.3 Resistors Combinations

2.1 Ohm’s Law 欧姆定律 Ohm's law states that the voltage v across a resistor is directly proportional to the current i flowing through the resistor. + - v i R （欧姆） Pay attention: resistor 电阻（名称） resistance 电阻值

Short Circuit: 短路 A short circuit is a circuit element with resistance approaching zero. R=0 i v=0 Network A short circuit (R = 0)

Open Circuit : 开路 An open circuit is a circuit element with resistance approaching infinity（无限大）. R= i=0 v Network An open circuit (R=)

v i Slope=R v i Slope=R The v~i characteristic （电压~电流特性）of: (a) a linear resistor, (b) a nonlinear resistor.

The power can be expressed in terms of R. Conductance (G) （电导） S(西门子） （姆欧） The power can be expressed in terms of R. NOTE : 1. The power is nonlinear function of either current or voltage. 2. A resistor always absorbs power （吸收功率）from the circuit. A resistor is a passive element.

Ⅰ. Nodes, Branches and Loops 结点，支路和回路 2.2 Kirchhoff‘s Laws 基尔霍夫定律 Ⅰ. Nodes, Branches and Loops 结点，支路和回路 A branch represents a single element such as a voltage source or a resistor. A node is the point of connection between two or more branches. A loop is any closed path in a circuit. A mesh (网孔）is a loop that contains no other loops within it. Independent nodes (独立的结点数) : 1 n-1 Independent loops (独立的回路数) 3 2 4

b=5 b=? n=3 n=? l=b-n+1=3 l=?

Ⅱ. Kirchhoff’s Laws 基尔霍夫定律 Kirchhoff’s current law （KCL 基尔霍夫电流定律） Kirchhoff’s current law states that the algebraic sum of currents entering a node (or a closed boundary) is zero.

or The sum of the currents entering a node is equal to the sum of the currents leaving the node.

Kirchhoff’s voltage law （KVL 基尔霍夫电压定律） Kirchhoff’s voltage law states that the algebraic sum of voltages around a closed path (or loop) is zero.

or Sum of voltage drops=Sum of voltage rises

Example 2.1 Calculate the current i in the circuit. Solution: 1 For loop 1, KVL gives i1 i2 For loop 2: KVL gives loop1 loop2 At node 1 : 2 then

Ⅰ. Series Resistors and Voltage Division 2.3 Resistors Combinations Ⅰ. Series Resistors and Voltage Division 串联电阻和分压 For N resistors in series The equivalent resistance of any number of resistors connected in series is the sum of the individual resistances.

Then voltage division （分压）

Ⅱ. Parallel Resistors and Current Division 并联电阻和分流 The equivalent resistance of N resistors connected in parallel:

The equivalent conductance of resistors connected in parallel is the sum of their individual conductances.

Two resistors in parallel current division （分流）

Ⅲ. Wye-Delta Transformations Y-转换 Balanced Wye-Delta Transformations

部分电路图和内容参考了： 电路基础（第3版），清华大学出版社 电路（第5版），高等教育出版社 特此感谢！