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Theoretical foundations of electrical engineering

# Loop method, example of the problem solving

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

Find
Currents in the branch by the loop method.

## Solution

Mark up randomly chosen directions of the currents, bypass circuits, circuit nodes.

Make matrix equation of the loop currents.
(Z)(I)=(U), where
(Z) — matrix of loop resistances;
(I) — matrix of unknown loop currents;
(U) — matrix of the electromotive force loops.

II=0,265 А;
III=0,347 А;
IIII=0,133 А;
IIV=0,273 А.

Having found all loop currents, we show through them currents in branches:
I1=II=0,265 А;
I2=III-II=0,347-0,265=0,082 А;
I3=III=0,347 А;
I5=II-IIII=0,265-0,133=0,132 А;
I6=III-IIII=0,347-0,133=0,214 А;
I7=IIV-IIII=0,273-0,133=0,140 А;
I8=-IIV=-0,273 А.

Found currents coincide with currents calculated using Kirchhoff’s laws that confirms the correctness of the solution
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