2.1 Ohm's Law

2.3 Resistors Combinations

2.2 Kirchhoff's Laws

Chapter 2 Basic Laws 基本定律

2.1 Ohm’s Law 欧姆定律

iv RR0

+ -v

i R

Ohm's law states that the voltage Ohm's law states that the voltage vv across a resistor across a resistor is directly proportional to the current is directly proportional to the current i i flowing flowing

through the resistor.through the resistor.

（欧姆）

resistorresistor

resistanceresistance

电阻（名称）

电阻值

Pay attention:

A short circuit is a circuit element with resistance approaching zero.

0

0

0

i

Riv

R

A short circuit (R = 0)A short circuit (R = 0)

RR=0=0

ii

v=0Network

Short Circuit: 短路

An open circuit is a circuit element with resistance approaching infinity （无限大） .

0

0

vR

vi

R

An open circuit (R=An open circuit (R=))

RR==

ii=0=0

vvNetwork

Open Circuit : 开路

v

i0

Slope=R

v

i0

Slope=R

The v~i characteristic （电压 ~ 电流特性） of:

(a) a linear resistor, (b) a nonlinear resistor.

iv R

NOTE :

1. The power is nonlinear function of either current or voltage.

v

i

RG

1

Conductance (G) （电导）

The power can be expressed in terms of R.

02

2 R

vRivip

S( 西门子）

（姆欧）

2. A resistor always absorbs power （吸收功率） from the circuit. A resistor is a passive element.

1 nbl

Ⅰ. Nodes, Branches and Loops 结点，支路和回路

Independent loops ( 独立的回路数 )

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 ) :n-1 1

2 3

4

2.2 Kirchhoff‘s Laws 基尔霍夫定律

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

Ⅱ. Kirchhoff‘s Laws 基尔霍夫定律

01

N

nni

Kirchhoff’s current law states that the algebraicKirchhoff’s current law states that the algebraic sum sum of currents entering a node (or a closed boundary) is zof currents entering a node (or a closed boundary) is zero.ero.

• Kirchhoff’s current lawKirchhoff’s current law （ KCLKCL 基尔霍夫电流定律）

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

outin ii

054321 iiiii

52431 iiiii or

Kirchhoff’s voltage law states that the algebraic sum of voltages around a closed path (or loop) is zero.

01

M

mmv

•Kirchhoff’s Kirchhoff’s voltagevoltage law law （ KKVVLL 基尔霍夫电压定律）

015432 vvvvv

or

41532 vvvvv

Sum of voltage drops=Sum of voltage rises

risedrop vv

Example 2.1 Calculate the current i in the circuit

012226 12 ii

0628 2 ii

021 iii

Solution:

For loop 1, KVL gives

For loop 2: KVL gives

At node 1 :

0628 2 ii

then A1i

i1 i2

loop1 loop2

2

1

Ⅰ. Series Resistors and Voltage Division

For N resistors in series

N

nnNeq RRRRR

121

The equivalent resistance of any number of resistors connected in series is the sum of the individual resistances.

2.3 Resistors Combinations

串联电阻和分压

2211 iRviRv

）（ 2121 RRivvv

voltage division （分压）

vRR

Rvv

RR

Rv

21

22

21

11

，

21 RR

vi

Then

Ⅱ. Parallel Resistors and Current Division 并联电阻和分流

The equivalent resistance of N resistors connected in parallel:

Neq RRRR /1/1/1/1 21

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

N

nnNeq GGGGG

121

Two resistors in parallel

iRR

Rii

RR

Ri

21

12

21

21

，

current division （分流）

Ⅲ. Wye-Delta Transformations Y- 转换

3

RRY

YRR 3

1 2

3

2R

3R

1R

1 2

3

12R

31R23R

1 2

3

YR YR

YR

1 2

3

R

RR

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！