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)
Principles of Physics: A Calculus-Based Text
5th Edition
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter21: Current And Direct Current Circuits
Section: Chapter Questions
Problem 67P: The values of the components in a simple series RC circuit containing a switch (Fig. P21.53) are C =...
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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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