2. A capacitor with capacitance C is connected in series to a resistor with resistance R and abattery with emf V. At t = 0, the circuit is complete.a. How much energy is stored in the capacitor when it is fully charged?b. The power output of the battery is P = iV, where i(t) = exp(-t/RC). Theinstantaneous energy supplied by the battery in an infinitesimal time dt is given as Pdt.Calculate the total energy supplied by the battery from t = 0 to when the systemreaches a steady state.c. The rate of consumption of electrical energy in the resistor is PR = i²R. In aninfinitesimal time interval dt, the amount of electrical energy consumed by the resistoris Prdt. Calculate the total energy consumed by the resistor from t = 0 to when thesystem reaches a steady state.d. What fraction of the total energy supplied by the battery is stored in the capacitor?e. What fraction of the total energy supplied by the battery is consumed in the resistor?

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