Find the current I3.

Correct option is C

Using Kirchhoff’s Current Law (KCL):
The relationship between the currents is given as: ​$$I_2 = I_3 - I_1$$

​​By applying Kirchhoff’s Voltage Law (KVL) in the left loop:
The equation becomes: $$10 - 3I_1 - 2I_3 = 0$$

$$3I_1 + 2I_3 = 10 \quad \text{... (a)}$$

​​By applying Kirchhoff’s Voltage Law (KVL) in the right loop:
The equation becomes: $$4I_2 + 2I_3 = 20$$

$$4(I_3 - I_1) + 2I_3 = 20$$

$$-4I_1 + 6I_3 = 20 \quad \text{... (b)}$$​       ​

Solving equations (a) and (b), the currents are:

$$I_1 = 0.769 \, \text{A}, \, I_2 = 3.071 \, \text{A}, \, I_3 = 3.84 \, \text{A}$$​