Q: Calculate the value of I₁ from the given circuit.

Solution:          We will redraw the circuit as shown below

For super node, constraint equation

                        V₁ - V₂ = 3

By applying KCL equation for super node

          (V₂ /6k) +   (V₁/3k) = 2 x 10-3

                     2V₁ + V₂ =12

Now value of V₂ from constraint equation

             V₂ = V₁- 3

Put the value of V₂ in the KCL equation of super node

                        2V₁ + V₁ - 3 = 12

                                    3V₁ = 15

                        V₁ = 5 V

Now 

                I₁ = ₁ 3k

                    =5/3k          // I=V/R, V₁ = 5V

                    =1.6 mA    Ans.