A capacitor C has been charged up to potential V0; at time t = 0, it is connected to a r...

A capacitor C has been charged up to potential V₀; at time t = 0, it is connected to a resistor R, and begins to discharge (Fig. 7.5a).

(a) Determine the charge on the capacitor as a function of time, Q(t). What is the current through the resistor, I (t)?

(b) What was the original energy stored in the capacitor (Eq. 2.55)? By integrating Eq. 7.7, confirm that the heat delivered to the resistor is equal to the energy lost by the capacitor. Now imagine charging up the capacitor, by connecting it (and the resistor) to a battery of voltage V₀, at time t = 0 (Fig. 7.5b).

(c) Again, determine Q(t) and I (t).

(d) Find the total energy output of the battery (? V₀I dt). Determine the heat delivered to the resistor. What is the final energy stored in the capacitor? What fraction of the work done by the battery shows up as energy in the capacitor? [Notice that the answer is independent of R!]

Equation 7.7

Figure 7.5