To reduce
the number of unknowns at the outset, the first rule of Kirchhoff is
used at every junction to assign the unknown current in each branch We then have three unknowns I1, I2 and I3 which can be found by
applying the second rule of Kirchhoff to three different closed loops Kirchhoff’s second rule for the closed loop ADCA gives,
10 – 4(I1– I2) + 2(I2 + I3 – I1) – I1 = 0
[3 61(a)]
that is, 7I1– 6I2 – 2I3 = 10
For the closed loop ABCA, we get
10 – 4I2– 2 (I2 + I3) – I1 = 0
that is, I1 + 6I2 + 2I3 =10
[3