Question 2.SA.3: Find the current through the 0.5 Ω resistor....

The voltage sources around the left loop are equal to the voltage drops across the resistances.

20 V − 19 V = 0.25 Ω i_1 + 0.4 Ω (i_1−i_2)

The same is true for the right loop.

19 V = 0.4 Ω (i_2−i_1) + 0.5 Ω i_2

Solve two equations and for two unknowns, using the simultaneous equation method:

0.65 Ω i_1 − 0.4 Ω i_2 = 1 V

−0.4 Ω i_1 + 0.9 Ω i_2 = 19 V

i_1 = 20 A

i_2 = 30 A

The current through the 0.5 Ω resistor is 30 A.