Find the current in each part of the circuit.

Explanation

Apply loop law in Fig. 5.81


(1) `-3I - 6I_1 +4.5 = 0 or I+2I_1 = 1.5 (i)`
(2) `10(I-I_1) +3 - 6I_1 = 0 or 10I - 16I_1 = -3 (ii)`
Solving Eqs. (i) and (ii) we get
`I = (1)/(2) A, I_1 = (1)/(2) A, and I-I_1 = (1)/(2) -(1)/(2) = 0`