Q:      Determine loop currents.

Solution:          We utilize the coupling equation technique to determine loop currents to find the loop currents.

                        Applying KVL equation for this super mesh

                                                        -7 +1(I₁ -I₂) +3(I₃ -I₂) +1I₃ =0

                                                                            I₁ -4I₂ +4I₃ =7   ...............(i)

                        And applying KVL eq for mesh2

                                                    1(I₂ -I₁)) +2I₂ +3(I₂ - I₃) =0

                                                                           -I₁ +6I₂ -3I₃ =0          ................(ii)

            Now Coupling equation

                                                        I₁ -I₃ = 7   .................(iii)         

                        By solving (i) & (ii)

                                                                            6I₁ -24I₂ +24I₃ = 42

                                                                          -4I₁ +24I₂ -12I₃ = 0

                                                                         2I₁ +12I₃= 42     ..............(iv)

                        Subtracting (ii) & (iv)

                                                               2I₁ +12I₃ = 42

                                                               2I₁ - 2I₃ = 14

                                                              14I₃ = 28

                                                              I₃ =2 A

                                                            Put this value in (a)

                                                                        I₁ -2 =7

                                                                           I₁ =9A

            and therefore I₂ can be determine by putting I₁ & I₂ in (i) or (ii) from 1

                                                9 - 4I₂ +8 =7

                                                  -4I₂ = -17 -7

                                                 4I₂ =10   => I₂ =2.5A