Solve the formula for the charging capacitor for q / qf = 0.99.
Solve the formula for the voltage across a charging capacitor for V / Vf = 5/12.
Differentiate the expression for the charge of a charging capacitor with respect to time to find the rate of change of charge. Evaluate at the time of interest.
For the rate of energy stored by the charging capacitor, differentiate the energy expression Q2 / 2C and use the above result.
Note that the rate of change of charge on the capacitor is the current in the circuit to be used for evaluation of the power dissipated by the resistor and the power delivered by the emf.
What time constant is needed for a capacitor to charge to 72 V in 0.50 seconds with an emf of 95 V?
To find the charge after the switch has been closed a long time, determine the "terminal voltage" of either of the emf+resistor branches. That is, after the capacitor is fully charged, there will still be a steady-state current in the outer loop, determined by the usual dc circuit approach.