At the steady state, the capacitor behaves as open circuit. The figure below represents the simple circuit,
Apply Kirchhoff law in loop I, −6+3(I1+I2)+2.8I1=0 5.8I1−3I2=6‌‌‌‌‌⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅(I) Apply Kirchhoff law in loop II, 2I2+3(I2−I1)=0‌‌‌‌‌⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅(II) From equation (I) and (II) I2=0.9A Thus, the current in 2Ω resistor is 0.9 A.