Note that the units associated with the resistor symbols are siemens, e.g. 1 S a

Question

Note that the units associated with the resistor symbols are siemens, e.g. 1 S and 2 S.

A) The value of the node voltage parameter 'a11' for this circuit is?

B) The value of both 'a12' and 'a21' in the node voltage equations is?

C) The value of the parameter 'a22' in the node voltage equations is?

D) Solving the node voltage equations for vA results in

E) Solving the node voltage equations for vB results in

Explanation / Answer

Greetings... By using KCL for Va: -2A+ Va* 2s + (Va-Vb)* 2s -2A=0 -----> then, 4Vb-2Va+2=0 ...(1) Solving for Vb: 2Vb-2Va+2Vb+2=0 ----> then, 4Vb-2Va+2=0 ....(2) By adding equations(1) & (2), we get: Va=1v and Vb= 0v Then substituting the values of Va and Vb to get: a11=4 and a21=-2 and by equating the following equations: 4=4*Va-2*Vb 4=a11*Va+a12*Vb Then a12=-2 and equating the following equations: -2=-2*Va+4*Vb -2=a21*Va+a22*Vb ---> then a22=4 Hope this solution was clear!

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