Q:  Determine the value of voltage V₀ .

 Solution:         We need to calculate the voltage V₀ . The circuit may be redrawn like

                                    By applying KVL equation for mesh 1

                                                            V_a + 4k(I₁ - I₂) =12

                                                            V_a +4kI₁ - 4kI₂ =12

                                    By applying KVL equation for mesh 2

                                                            4Va +6kI2 + 4k(I2 - I1)=0

                                                                   4Va +10kI₂ - 4kI₁ =0

                        Here from the circuit

                                                            V_a =2kI₁

                        By putting V_a  value in the equation of mesh 1 we will obtain

                                                                        2kI₁ + 4kI₁ - 4kI₂ =12

                                                                                    6kI₁ - 4kI₂ =12

                        Afterwards putting the value of V_a in the equation of mesh 2

                                                                        8kI₁ + 10kI₂ - 4kI₁ = 0

                                                                                  4kI₁ + 10kI₂ = 0

Now by multiplying modified equation of mesh 1 by 1.5 & by subtracting modified equation of mesh 2 from modified equation of mesh 1

                                                                        6kI₁ - 4kI₂ = 12

                                                                        - 6kI₁ - 15kI₂= 0

                                                                           - 19kI₂ =12

                                                                        I₂ = -12/19 =0.6315 mA

                        Now                 V₀ = 6k x .6315

                                                   V₀ = 3.78 V