An RC circuit like the one shown in figure 25.18 (a series RC circuit charging a capacitor) has a 2.0μF capacitor, a 2.2k resistor, and a 12 V constant voltage source (battery). (a) Write the equations for the current as a function of time and the voltage across each component as a function of time. (b) Write the equations for the power going into or out of each component as a function of time. (c) The total energy (provided by the source, dissipated by the resistor, stored by the capacitor) is the time integral of the power (of battery, resistor, capacitor, respectively.) Integrate the power equations you wrote (over all time, from 0 to infinity - technically, steady state is at infinite time!) to find the energy transfer associated with each component. 1- (d) Check: is energy conserved? That is, does the total energy provided by the source equal to the energy dissipated by the resistor plus the energy stored in the capacitor? Does the fraction of the total energy provided by the battery that ends up stored in the capacitor depend on the value of the resistance and/or the capacitance? Is the energy in the capacitor 1/2CV2 as expected?

An RC circuit like the one shown in figure 25.18 (a series RC circuit charging a capacitor) has a 2.0μF capacitor, a 2.2k resistor, and a 12 V constant voltage source (battery). (a) Write the equations for the current as a function of time and the voltage across each component as a function of time. (b) Write the equations for the power going into or out of each component as a function of time. (c) The total energy (provided by the source, dissipated by the resistor, stored by the capacitor) is the time integral of the power (of battery, resistor, capacitor, respectively.) Integrate the power equations you wrote (over all time, from 0 to infinity - technically, steady state is at infinite time!) to find the energy transfer associated with each component. 1- (d) Check: is energy conserved? That is, does the total energy provided by the source equal to the energy dissipated by the resistor plus the energy stored in the capacitor? Does the fraction of the total energy provided by the battery that ends up stored in the capacitor depend on the value of the resistance and/or the capacitance? Is the energy in the capacitor 1/2CV2 as expected?

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter29: Direct Current (dc) Circuits

Section: Chapter Questions

Problem 76PQ

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