§ 1-3 Kirchhoff's laws
A point at which two or more elements have common
connection is called a node(节点 ),
Suppose that we start at one node in a network and
move through a simple element to the node at the
other…,if no node was encountered more than once,
then the set of nodes and elements that we have passed
through is defined as a path（ 路径 ）,
1
2
3 3
1
2
a b
We define a branch（ 支路 ） as a single path in a
network,composed of one simple element and the
node at each end of that element.
Kirchhoff's current law --KCL
The algebraic sum of all
the currents entering any
node is zero.
If the node at which we started is the same as the
node on which we ended,then the path is a closed path
（ 闭合路径 ） or a loop（ 回路 ）,
0??? CBA iii
Ai Bi
Ci
The algebraic sum of all the currents leaving a node
is zero,or the algebraic sum of all the currents entering
a node must equal the algebraic sum of all the currents
leaving the node.
04321 ???? iiii
04321 ????? iiii
4321 iiii ???
The three equivalent equations
The algebraic sum of all the currents entering any
node is zero.
1i
2i
3i4i
00 2
1
1 ??????
?
N
N
n
n iiiori ?
KCL:
The KCL may be extended to the supernode.
01 12311 ??? iii:n o d e
02 23122 ??? iii:n o d e
03 31233 ??? iii:n o d e
0321 ??? iii:er n o d es u p
1i
2i
3i
12i
23i
31i
1
2
3
The algebraic sum of the voltage around any closed
path in a circuit is zero.
Kirchhoff's voltage law--KVL
A
B
?
?
??
1?
2?
0,21 ??? ??c l ok w i s e
0,21 ?? ??kw i s ec ou n t e r c l o
00 2
1
1 ??????
?
N
N
n
n or ???? ?
KVL:
?? 2?
?
?
?
?1
? 3?
0,321 ???? ???c l o k w i s e
0,321 ??? ???k w i s ec o u n t e r c l o