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.

University Physics Volume 2

18th Edition

ISBN:9781938168161

Author:OpenStax

Publisher:OpenStax

Chapter9: Current And Resistance

Section: Chapter Questions

Problem 84CP: In this chapter, most examples and problems involved direct current (DC). DC circuits have the...

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