write a matrix equation that determines the loop currents. Also enter positive values for positive voltages and negative values for negative voltages

Question

you have 4 loops

loop 1 has a voltage of 22

Resistors: 3, 1,3 and 5 (which is shared with loop 2)

Loop 2 has a voltage of 30

resistors: 2,5( which is shared with loop 1), 3, 2

Loop 3 has a voltage of 20

Resistors: 3, 2 (which is shared with loop 2), 4,1

Loop 4 has a voltage of 22

Resistors: 2,1 (which is shared with loop 3), 2,3

[ ]

[ ] =

[ ]

[ ]

Answer 1

For each current loop, i_n, it will be the sum of all the loop resistances time i_n minus the sum of IR voltages of shared loop resistances. The sum will be equal to the given loop voltage.

[ 12 -5 0 0] [i₁] = [22]

[ -5 12 -2 0] [i₂] = [30]

[ 0 -2 10 -1] [i₃] = [20]

[ 0 0 -1 8] [i₄] = [22]

If A is the resistance matrix, C is the current vector and V is the voltage vector

AC=V

C=A^-1V

Answer 2

Do you have a circuit diagram of this?