


KCL states that the algebraic sum of the currents in all the branches which converge in a common node is equal to zero
SI_{in} = SI_{out}
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
Solution example from circuit magic.
Writing Kirchhoff current law for 31 nodes
(Note number of Kirchhoff current laws equations equal Nodes Number –1)
(Node 1)J1+I3+I4+I7=0
(Node 2)J1+I2I4=0
Wrining Kirchoff voltage law for 51(31) loops
(Loop1) I3·R3I7·R5=E2
(Loop2) I2·R2I7·R5+I4·R4=E1E2
Linear equations
I3+I4+I7=2
I2I4=2
10I310I7=10
11I2+10I410I7=7
Equations solution
I1=2
I2=0,692
I3=0,846
I4=1,308
I7=0,154
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