Exponential decay Current A When discharging the capacitor

Exponential decay Current μA When discharging the capacitor, the current time graph has this particular form. It is exponential in form. (The “mathematical” form of a curve like this never actually falls to zero though in practice it does). Time s

Exponential decay The equation of the curve can be shown to be I o Current μA Time s Where C is the capacitance of the capacitor and R is the resistance of the FIXED series resistor

Exponential decay Charge stored μC The form of the graph is exactly the same for the charge stored on the capacitor. We can multiply both sides of the equation by t As Q=It we have Time s This is the form you find the equation in in your specification

Exponential decay Note that the only variable on the right is t. When t=CR Charge stored μC e = 2. 718 so 1/e = 0. 368 Time s So C x R is an important value and is known as the time constant.

Exponential decay Current μA Io Q = 0. 368 Qo 0. 368 Io (0. 368)2 Io (0. 368)3 Io RC 2 RC Time s 3 RC The time it takes the current to fall by a factor of 1/e is a constant. That time interval is RC the time constant. What are the units of the time constant?

Calculate the time constant in each case: R/Ω C/μF A 1000 500 B 1 000 C 1 000 240 In each case calculate the length of time it would take A B C and D to fall to a)0. 638 b) 0. 135 of its initial value? Time const/