§1-3 Kirchhoffs 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 hrough is defined as a pati(路径)
§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
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) 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 L,十 十 0
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）. i A + i B + i C = 0 A i B i C i
The algebraic sum of all the currents entering any node is zero 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. i1+2-i2-i4=0 i1-2+2+i4=0 1+l2=3+4 The three equivalent equations
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. 0 1 2 3 4 i + i − i − i = 0 1 2 3 4 − i − i + i + i = 1 2 3 4 i + i = i + i The three equivalent equations The algebraic sum of all the currents entering any node is zero. 1 i 2 i 3 i 4 i
KCL. ∑in=0ori1+i2+…+iN=0 The Kcl may be extended to the supernode nodel.i,++ 12s 0 nOe2:i2+i12-i23=0 nodes 3 23 31 0 suPernode +i t 0
0 2 0 1 = 1 + + + = = N N n n i or i i i KCL: The KCL may be extended to the supernode. node1 : i 1 + i 31 − i 12 = 0 node2 : i 2 + i 12 − i 23 = 0 node3 : i 3 + i 23 − i 31 = 0 supernode : i 1 + i 2 + i 3 = 0 1 i 2 i 3 i 12 i 23 i 31 i 1 2 3
Kirchhoff s voltage law--KVL The algebraic sum of the voltage around any closed path in a circuit is zero. clokwise-0,+U=0 counterclockwise: D1-D2=0 KVL. ∑ U,=0orU1+U,+…+U 0 D clockwise: -D1 +02-U3=0 十 counterclockwise U-2+U3=0 十
The algebraic sum of the voltage around any closed path in a circuit is zero. Kirchhoff' s voltage law--KVL A B + + − − 1 2 clokwise:−1 +2 = 0 counterclokwise :1 −2 = 0 0 2 0 1 = 1 + + + = = N N n KVL: n or +2 − + + − − 1 3 clokwise : −1 +2 −3 = 0 counterclokwise :1 −2 +3 = 0