Energy and Power in an RC Circuit. See the figure. With the switch in position A, the capacitor becomes charged. After a long time, the capacitor charge approaches q = Ce. Now, suppose the capacitor is fully charged. When, at time t = 0, the switch is moved from A to B.
(A) Determine the charge q(t) and current i(t) for t > 0.
(B) Determine the energy of the capacitor U(t) as a function of time t. The initial energy, at t = 0, is Uo. Calculate the energy at t = RC and at t = 0.56 RC. Express the answers as fractions of the initial energy (No units because the answers are a ratio of energy/energy).
(C) Determine the power P(t) dissipated in the resistor. Calculate the power at t = RC and t = 0.56 RC. Express the answers as fractions of Uo/T.
(D) Determine the integrated power (the integral of P(t') from t' = 0 to t). Calculate the integrated power for t = RC and t = 0.56 RC. Express the answers as fractions of Uo.