Q:  Compute the value of V₀ & I₀.

Answer:

Node 2 & 3 constitute a super node Constraint equation is

                                 V₂ - V₃ = 6 ..........(1)

Applying KCL equation at super node

                        ((V₂-12)/6k) + (V₂/3k) + (V₃ /6k) + ((V₃ -12)/12k) =0

                        (V₂/6k) + (V₂/3k) +(V₃ /12k) + (V₃ /6k) - (12/12k) - (12/6k) = 0

                               (V₂/2k) + (V₃ /4k) - (12/4k) =0

                                         2V₂ +V₃ - 12 = 0

                                              2V₂ + V₃ = 12 ---- (2)

Now value of V₃ from constraint equation (1) is

                                          V₃ =V₂ -6

Put the value of V₃ in equation (2)

The super node equation will becomes

                                     2V₂ +V₂ -6 =12

                                            3V₂ = 18

                                          V₂    =18/3 = 6 Volts

Put this value in super node equation

                                    V₃ =0

                                  So,

                                    Vo =0

                                 I₀ = V2/3k

                                    =6/3k

                                       =2mA