How capacitor values are determined in this circuit
the current of 11.2mA you calculated from the equation I=C*ΔV/ΔT has no matter here because the ripple voltage and main freq are related to a rectifer circuit based on bridge diodes. Here the 47uF capacitor is a charge supply connected to Q2 emitter and the motor's current is directly controlled by Q2 wich is controlled by Q1, the collector current of Q2 is Ic2 = I1+I2 I1 flows through R4 while I2 wich flows hrough R3 is flowing through motor and R5. Hence the motor current is taken from the 5v supply and transistor Q2 is controlling its ammount.