The circuit in the figure incorporates a C-R network, a 9V battery and a 1pole, 2-way switch. All the values for resistors and capacitor are shown in the figure. The switch has been in position \( \mathrm{A} \) long enough to assume that the capacitor \( \mathrm{C} \) is fully charged.
i) What is the magnitude of the charge stored by capacitor \( \mathrm{C} \) ?
ii) If the switch is now thrown to position \( \mathrm{D} \), what is the time constant of the circuit ?
iii) Calculate the time it takes for the capacitor to discharge to \( 2.5 \mathrm{~V} \). Show all your calculations.