4 a capacitor of capacitance c 120 mf is charged using a battery of 24

Question

4. A capacitor, of capacitance C = 120 μF is charged using a battery of 24 V. The internal resistance of the battery is 100 2. Once charged, the capacitor is connected to the circuit presented in the figure below. It is known that R₂=2R₁, R3=2R2, and R3 = 40052. The value of R₂ is unknown.
(a) Calculate how long it takes for the capacitor to be 99% charged and determine the initial charge on the capacitor.
(b) Just after connecting the capacitor C, at time t = 0, the current through R₂ is 1A. Calculate the value of R, and the energy stored in the capacitor at t = 0.
(c) The resistor network, R₁, R2, R3 and R₂, can be replaced by a single equivalent resistance. Find this equivalent resistance and hence find the time constant of the discharging circuit.
(d) Find the time t, after which the electric charge on C drops by a factor of 2 and calculate the energy dissipated in the circuit in time 12.
(e) Calculate the energy dissipated on R, after a very long time.