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 = C?.
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 $U_0$. 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.)
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(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 $U_0/T$.
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(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 $U_0$.
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