A series circuit consists of a resistor and capacitor of resistance R ohms and capacitance C Farads. It has the battery as a source of E volts. When the switch is closed the capacitor begins to charge and the total charge on the capacitor at any time q (t) is governed by: dq(t)/dt+(1/RC)q(t)=E/R where R, C, E are taken as constant. Find the charge q (t) across the capacitor at any time t. Hence show that as t → ∞, E = q(t)/c (Note that at t=0,q(t)=0)
A series circuit consists of a resistor and capacitor of resistance R ohms and capacitance C Farads. It has the battery as a source of E volts. When the switch is closed the capacitor begins to charge and the total charge on the capacitor at any time q (t) is governed by: dq(t)/dt+(1/RC)q(t)=E/R where R, C, E are taken as constant. Find the charge q (t) across the capacitor at any time t. Hence show that as t → ∞, E = q(t)/c (Note that at t=0,q(t)=0)
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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A series circuit consists of a resistor and capacitor of resistance R ohms and capacitance C Farads. It has the battery as a source of E volts. When the switch is closed the capacitor begins to charge and the total charge on the capacitor at any time q (t) is governed by: dq(t)/dt+(1/RC)q(t)=E/R where R, C, E are taken as constant. Find the charge q (t) across the capacitor at any time t. Hence show that as t → ∞, E = q(t)/c
(Note that at t=0,q(t)=0)
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