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Theoretical foundations of electrical engineering

# Calculation of current circuits with the help of the first and second Kirchhoff’s laws (KCL and KVL)

Given
R1=16 ohms;
R2=31 ohms;
R3=24 ohms;
R4=13 ohms;
R5=33 ohms;
R6=40 ohms;
R7=22 ohms;
R8=7 ohms;
E1=30 V;
E2=24 V;
E7=16 V;
E8=11 V.

Find
Currents in the circuit with the help of Kirchhoff’s laws.

## Solution We make equations according to Kirchhoff’s laws. The first Kirchhoff’s law says that the sum of entering and leaving currents at any node is equal to zero. The second Kirchhoff’s law says the algebraic sum of the potential differences in a circuit loop is equal to the sum of the electromotive force in this loop. There are m=7 branches and n=4 nodes in the given scheme. Therefore, according to the first Kirchhoff’s law n-1 = 3 equations must be made , and according to the second Kirchhoff’s law m-(n-1)=4 equations must be made. We mark randomly chosen currents directions, bypass circuits, circuit nodes.   Answer:
I1=0,265 А; I2=0,082 А; I3=0,347 А; I5=0,131 А; I6=0,214 А; I7=0,140 А; I8=-0,273 А.

Found currents coincide with currents, calculated using the method of mesh or loop current that confirms the correctness of the solution.
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