A capacitor with capacitance C is connected in series to a resistor with resistance R and a battery 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) = Inexp(-t/RC). The instantaneous 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 system reaches a steady state. c. The rate of consumption of electrical energy in the resistor is PR = i²R. In an infinitesimal time interval dt, the amount of electrical energy consumed by the resistor is Prdt. Calculate the total energy consumed by the resistor from t = 0 to when the system reaches a steady state. d. What fraction of the total energy supplied by the battery is stored in the capacitor?
A capacitor with capacitance C is connected in series to a resistor with resistance R and a battery 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) = Inexp(-t/RC). The instantaneous 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 system reaches a steady state. c. The rate of consumption of electrical energy in the resistor is PR = i²R. In an infinitesimal time interval dt, the amount of electrical energy consumed by the resistor is Prdt. Calculate the total energy consumed by the resistor from t = 0 to when the system reaches a steady state. d. What fraction of the total energy supplied by the battery is stored in the capacitor?
Related questions
Question
Transcribed Image Text:2. A capacitor with capacitance C is connected in series to a resistor with resistance R and a
battery 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). The
instantaneous 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 system
reaches a steady state.
c. The rate of consumption of electrical energy in the resistor is PR = i²R. In an
infinitesimal time interval dt, the amount of electrical energy consumed by the resistor
is Prdt. Calculate the total energy consumed by the resistor from t = 0 to when the
system 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?
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps with 2 images
