Discharging Capacitor: Kirchoff's loop rule applied to the discharging capacitor circuit gives 2- C AV₁ =1 = IR - = 0 loop The current is leaving the positive plate so I = -dQ/dt = -CdAV/dt. Substituting this into loop rule gives a differential equation for Q(t): davc RC + AV = 0 dt R www C This is the simplest differential equation you will learn in your differential equations class. The solution for the differential equation for AVC (t) is an exponential: AV (t) = AV e-t/(RC) (discharging) where AV, is the voltage across the capacitor when discharge begins (t = 0). The quantity Tc = RC has dimensions of time and is called the time constant of the circuit. It describes how long it takes for the capacitor to charge or discharge. 2. Show that a ohm farad is the same as a second. Show steps.

Discharging Capacitor: Kirchoff's loop rule applied to the discharging capacitor circuit gives 2- C AV₁ =1 = IR - = 0 loop The current is leaving the positive plate so I = -dQ/dt = -CdAV/dt. Substituting this into loop rule gives a differential equation for Q(t): davc RC + AV = 0 dt R www C This is the simplest differential equation you will learn in your differential equations class. The solution for the differential equation for AVC (t) is an exponential: AV (t) = AV e-t/(RC) (discharging) where AV, is the voltage across the capacitor when discharge begins (t = 0). The quantity Tc = RC has dimensions of time and is called the time constant of the circuit. It describes how long it takes for the capacitor to charge or discharge. 2. Show that a ohm farad is the same as a second. Show steps.

College Physics

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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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Question

Discharging Capacitor: Kirchoff's loop rule applied to the discharging capacitor circuit gives
Q
ΣAV₁ =
loop
= IR-
= 0
The current is leaving the positive plate so I = -dQ/dt = -CdAVc/dt. Substituting
this into loop rule gives a differential equation for Q(t):
RC + AVc = 0
dAvc
dt
This is the simplest differential equation you will learn in your differential equations
class. The solution for the differential equation for AVC (t) is an exponential:
R
www
C
AV (t) = AV e-t/(RC)
(discharging)
where AV, is the voltage across the capacitor when discharge begins (t = 0). The quantity Tc = RC has dimensions of
time and is called the time constant of the circuit. It describes how long it takes for the capacitor to charge or discharge.
2. Show that a ohm farad is the same as a second. Show steps.

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