B2. (a) The voltage discharging characteristic of a capacitor in a resistance-capacitance circuit is shown as follows: Vc=V0et where time constant =RC Given that Vo is the initial voltage of the capacitor, while R and C are constant. (i) Find the time constant when t=0.5sec,Vc=0.3Vo (3 marks) (ii) Find the time of discharging from Vc=0.9Vo to Vc=0.1Vo (5 marks) (iii) If time constant is double, find the time of discharge for (5 marks) Vc=0.2Vo (b) The amount of carbon-14 contained in a fossil is modeled by the equation C(t)=10e0.000121t - C is the amount of carbon-14 in micrograms ( g) - t is time in years Calculate: (i) The initial amount of carbon-14 in the fossil. (2 marks) (ii) The time passed if the amount of carbon-14 right now is half ( 5 marks)