A network N consists of resistors, independent voltage and current sources. The value of its determinant based on the loop analysis:

1. cannot be negative

2. cannot be zero

3. is independent of the values of voltage and current sources

4. dependent on the values of the resistances and the voltage and current sources

Mesh Analysis:

Mesh analysis is a method of analyzing network with the help of KVL equations.

For a network having N nodes and B branches, the number of simultaneous equations to be solved to get the unknowns

= Number of KVL equations

= number of independent loop equations

= B - N + 1

B = Number of branch

N = Number of node

For example, we take the circuit.

Apply KVL in loop 1

V₁ = R₁ I1 + R₂ (I1 + I2)

V₁ = (R₁ + R₂) I₁ + R₂ I₂  _____equation (1)

Apply KVL in loop 2

V₂ = R₃ I2 + R₂ (I₁ + I2 )       

V₂ = R₂ I₁ + (R₂ + R₃) I₂ _____equation (2)

In the matrix form

\(\left[ {\begin{array}{*{20}{c}} {{V_1}}\\ {{V_2}} \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} {{R_1} + {R_2}}&{{R_2}}\\ {{R_2}}&{{R_2} + {R_3}} \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {{I_1}}\\ {{I_2}} \end{array}} \right]\)

The determinant of the matrix Can not be zero and or negative and does not depends on the value of voltage or current.

\(\left[ {\begin{array}{*{20}{c}} {{R_1} + {R_2}}&{{R_2}}\\ {{R_2}}&{{R_2} + {R_3}} \end{array}} \right]\)