Q: Calculate the value of current Io through the 10k ohm resistor also determine V₁ & V₂.

 Solution:

                              I₀= V₁/10k ..................(A)

Here V₁ is the voltage for node 1. We need to calculate the node voltages.

Therefore, at node 1

                ((V₁- V₂)/10k)  + (V₁/10k) = 4mA

      (V₁/10k) + (V₁/10k) - (V₂/10k) = 4mA

                        Put the value of I₀    in equation

                                      I₀ + I₀ - (V₂/10k) = 4mA        // V1= 10 I₀

                                            2 I₀ - (V₂/10k) = 4mA

                                             20 I₀ -V₂ =40mA .........(B)

Now at node 2

                                    (V₂/10k) + ((V₂ - V₁)/10k) = -2I₀

                                      (V₂/10k) + (V₂/10k)  -  (V₁/10k) = -2I₀

                                                (V₂/10k)+     (V₂/10k) - I₀ = -2I₀

                                                   2V₂ + 10I₀ = 0 .........(C)

Equating equations of node 1 & 2

                                                        40 I₀ - 2V₂ = 80mA

                                                              10 I₀ + 2V₂ = 0

                                                            50 I₀   = 80mA      

Thus,                                         I₀ = 8/5 mA 

Therefore, putting the value of I₀ in equation (A)

                                            I₀ = (V₁/10k)

                                    8/5 mA = (V₁/10k)

                                    V₁ = 16 volts

                        put the value of I0 from (A) to (C) we get

                                                       2V₂ + V₁ =0

                                                             2V₂ =-V₁

                                                               V₂ = -16/2 = -8 V