Kirchhoff's Current Law (KCL)
KCL states that the algebraic sum of the currents in all the branches which
converge in a common node is equal to zero
SIin =
SIout
Kirchhoff's Voltage Law
Kirchhoff's Voltage Law states that the algebraic sum of the voltages between
successive nodes in a closed path in the network is equal to zero.
SE =
SIR
Solution using Kirchhoff�s Voltage and current laws
Steps to solve circuit by Kirchhoff�s Laws.
1. Construct circuit with circuit magic schematics editor.
Circuit sample from circuit
magic.
2. Construct loops. (See
�creating loop� section in user guide) Number of loops (and
number of Kirhhoff�s Voltage laws equations) can be determined using following
formula. Loop can not include branches with current sources. Due current sources
resistance equal infinity.
Loop Number = Branch Number �(Nodes Number �1) � Current
sources Number
3. Select Analyze->Solve by
Kirhhoff�s laws menu item
4. In dialog box press OK button. if no warning shown.
5. Read solution.
Solution example from circuit magic.
Writing Kirchhoff current law for 3-1 nodes
(Note number of Kirchhoff current laws equations equal Nodes Number �1)
(Node 1)J1+I3+I4+I7=0
(Node 2)-J1+I2-I4=0
Wrining Kirchoff voltage law for 5-1-(3-1) loops
(Loop1) I3�R3-I7�R5=-E2
(Loop2) I2�R2-I7�R5+I4�R4=E1-E2
Linear equations
I3+I4+I7=-2
I2-I4=2
10I3-10I7=-10
11I2+10I4-10I7=-7
Equations solution
I1=2
I2=0,692
I3=-0,846
I4=-1,308
I7=0,154
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