State Kirchhoff’s rules of current distribution in an electrical network. Using these rules determine the value of the current I₁ in the electric circuit given below.

For electrical network, Kirchhoff’s rules are as follows:

(i) Junction rule: At any junction, the sum of the currents entering the junction is equal to the sum of currents leaving the junction
                   ∴ Σ I = 0

(ii) Loop rule: The algebraic sum of changes in potential around any closed loop involving resistors and cells in the loop is zero.
           ∴ Σ IR + Σ E = 0

According to Kirchhoff’s rule, I₁ + I₂ = I₃

In the given circuit, 
Applying loop rule to both the lower and upper loops, we get 

40 I₃ + 20 I₁ = 40          (In loop ABCF)
40 I₃ + 20 I₂ = 80 + 40  (In loop CDEF)

Adding these two equations, we get
               $80 {\mathrm{I}}_3 + 20({\mathrm{I}}_1+{\mathrm{I}}_2) = 160$

                     $80 {\mathrm{I}}_3 + 20 {\mathrm{I}}_3 = 160$ 
           
                                    $$\begin{gathered} {\mathrm{I}}_3 = \frac{160}{100} \\ = 1.6 \mathrm{A} \end{gathered}$$ 

Putting the value of I₃ in the above equation to find the value of I₁, we get

          $40 \times 1.6 + 20 {\mathrm{I}}_1 = 40$

            $20 {\mathrm{I}}_1 = 40-64 = -24$

                  ${\mathrm{I}}_1 = -\frac{24}{20} = -1.2 \mathrm{A}.$