As at t=0 switch is open so initially capacitor is uncharged.So,we use equation of charging of capacitor in an RC Circuit which is:
here =CE where c is the capacitance= and e=battery potential =24 v (according to given question)
and T=time constant =RC i.e. product of resistance and capacitance = 54micro seconds (according to given question)
so maximum charge==144 micro coulomb.
current in the circuit after t seconds is given by following equation
=2.66*e^(-10/.000054)=0A as the capacitor is fully charged.