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Circuit Analysis 3:
Application of KVL and KCL and Matrix 4 x 4

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Circuit Analysis 3:
Application of KVL and KCL and Matrix 4 x 4







SOLVE FOR THE CURRENT VALUE OF X , Y, Z. You may wish to verify in your electronic lab kit the actual current flowing in each loop.

Application of four simultaneous linear equations

X = A
Y = A
Z = A
X +
Y +
Z +
W
= At Node A, KCL
X +
Y +
Z +
W
= At Node B, KCL
4 X +
2 Y +
Z +
W
= 8
Loop 1 , KVL
X +
2 Y +
5 Z +
W
= 9
Loop 2, KVL

INITIAL CONDITION:

Answer, X = 1 A detX =

Answer, Y = 2 A detY =

Answer, Z = 1 A detZ =

Answer, W = detW =

determinant 4 x 4 =

Validate your answer by substituting the value of X, Y, and Z in original equations.


You need to complete all the input box then NaN (Not a Number) error message will be fixed. Automatic computation

4 Ω value change to 7 ohms 4 Ω Loop 1
2 Ω value change to 20 ohms 2 Ω Loop 1
3 Ω value change to 6 ohms 3 Ω Loop 2
2 Ω value change to 8 ohms 2 Ω Loop 2
8 volts value change to 10 volts 8 Volts original
V9 value UNCHANGE 9 Volts original


Reviewer on how to compute for determinant value of 4 x 4 Matrix.

Acquiring knowledge and skill on how to solve for determinant of 4 x 4 matrix is important in solving any four simultaneous linear equation. In the above example, determinant X ( detX), detY, detZ, and detW were computed. Then following Cramer's Rule, the solution for value of X, Y , Z, and W can be calculated. Doing this calculation by hand is very time consuming but thanks to computer and internet advancement, it is now possible to solve this problem in less than a minute using your smartphone. Now our brain can be used for higher level of thinking such as scenario analyis and decision making.

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